Mathematics
Grade9
Easy

Question

Graph the reflection of the polygon in the given line: y = -x

hintHint:

Plot the given points on the graph and then obtain the points of reflection efficiently.

The correct answer is:


    * In Geometry, a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection.
    *It is a type of transformation that produces mirror image of the shape.
    The reflection transformation can be done in many ways.
    *Reflection over X-axis
    *Reflection over Y-axis
    *Reflection over Y = X
    Given That:

    >>>let (a, b) be a point on the x-y plane. Then, the point of reflection with respect to y=-x becomes (-b, -a).
    >>>Therefore, the point of reflection's for the vertices of triangle A(-6,-4);B(-5,-1);C(-3,-2) are:
    A'(4,6);B'(1,5);C'(2,3).
    >>>Then, the graph becomes:

    If (a, b) is reflected in the line y = -x, its image is the point (-b, -a).
    (a, b) → (-b, -a)
    A (-6, -4)  → (4, 6)
    B (-5, -1) → (1, 5)
    C (-3, -2) → (2, 3)

    Related Questions to study

    Grade9
    Mathematics

    Graph the reflection of the polygon in the given line: y = x

    If (a, b) is reflected in the line y = x, its image is the point (b, a).
    (a, b) → (b, a)
    A (-6, -4)  → (-4, -6)
    B (-5, -1) → ( -1, -5)
    C (-3, -2) → (-2, -3)

    Graph the reflection of the polygon in the given line: y = x

    MathematicsGrade9

    If (a, b) is reflected in the line y = x, its image is the point (b, a).
    (a, b) → (b, a)
    A (-6, -4)  → (-4, -6)
    B (-5, -1) → ( -1, -5)
    C (-3, -2) → (-2, -3)

    Grade9
    Mathematics

    The vertices of a triangle are A (2, 3), B (6, 1) and C (7, 5). Graph the reflection of the triangle ABC in the given line y = 3

    Point A is on the line, so its reflection is also on the same line (2, 3)
    Point B is 2 units below the line, so its reflection is 2 units above the line at B’ (6, 5).
    Point C is 2 units above the line, so its reflection is 2 units below the line at C’ (7, 1).

    The vertices of a triangle are A (2, 3), B (6, 1) and C (7, 5). Graph the reflection of the triangle ABC in the given line y = 3

    MathematicsGrade9

    Point A is on the line, so its reflection is also on the same line (2, 3)
    Point B is 2 units below the line, so its reflection is 2 units above the line at B’ (6, 5).
    Point C is 2 units above the line, so its reflection is 2 units below the line at C’ (7, 1).

    Grade9
    Mathematics

    The vertices of a triangle are A(2,3), B (6,1) and C(7,5). Graph the reflection of the triangle ABC in the given line x-axis.

    Point A is 2 units above the line, so its reflection is 2 units below the line at A’ (2, -3).
    Point B is 1 unit above the line, so its reflection is 1 unit below the line at B’ (6, -1).
    Point C is 5 units above the line, so its reflection is 5 units below the line at C’ (7, -5).

    The vertices of a triangle are A(2,3), B (6,1) and C(7,5). Graph the reflection of the triangle ABC in the given line x-axis.

    MathematicsGrade9

    Point A is 2 units above the line, so its reflection is 2 units below the line at A’ (2, -3).
    Point B is 1 unit above the line, so its reflection is 1 unit below the line at B’ (6, -1).
    Point C is 5 units above the line, so its reflection is 5 units below the line at C’ (7, -5).

    parallel
    Grade9
    Mathematics

    Graph the image of the triangle ABC, if A (-4, 0), B (-3, 3) and C (-1, 2), which is reflected along y= -x.

    If (a, b) is reflected in the line y = -x, its image is the point (-b, -a).
    (a, b) → (-b, -a)
    A (-4, 0)  → A’(0,4)
    B(-3, 3) → B’(-3, 3)
    C(-1, 2) → C’(-2, 1)
    Image coordinates of the triangle ABC are A’(0,4), B’(-3, 3) and C’(-2, 1).

    Graph the image of the triangle ABC, if A (-4, 0), B (-3, 3) and C (-1, 2), which is reflected along y= -x.

    MathematicsGrade9

    If (a, b) is reflected in the line y = -x, its image is the point (-b, -a).
    (a, b) → (-b, -a)
    A (-4, 0)  → A’(0,4)
    B(-3, 3) → B’(-3, 3)
    C(-1, 2) → C’(-2, 1)
    Image coordinates of the triangle ABC are A’(0,4), B’(-3, 3) and C’(-2, 1).

    Grade9
    Mathematics

    Find the image coordinates of the triangle ABC, if A (-4, 0), B (-3, 3) and C (-1, 2), which is reflected along x-axis.

    If (a, b) is reflected in the x-axis, its image is the point (a, -b).
    (a, b) → (a, -b)
    A (-4, 0)  → A’ (-4, 0)
    B (-3, 3) → B’ (-3, -3)
    C (-1, 2) → C’ (-1, -2)
    Image coordinates of the triangle ABC are A’ (-4, 0), B’ (-3, -3) and C’ (-1, -2).

    Find the image coordinates of the triangle ABC, if A (-4, 0), B (-3, 3) and C (-1, 2), which is reflected along x-axis.

    MathematicsGrade9

    If (a, b) is reflected in the x-axis, its image is the point (a, -b).
    (a, b) → (a, -b)
    A (-4, 0)  → A’ (-4, 0)
    B (-3, 3) → B’ (-3, -3)
    C (-1, 2) → C’ (-1, -2)
    Image coordinates of the triangle ABC are A’ (-4, 0), B’ (-3, -3) and C’ (-1, -2).

    Grade9
    Mathematics

    Find the image coordinates of the triangle ABC, if A (-4, 0), B (-3, 3) and C (-1, 2), which is reflected along y = -x.

    If (a, b) is reflected in the line y = -x, its image is the point (-b, -a).
    (a, b) → (-b, -a)
    A (-4, 0)  → A’ (0, 4)
    B (-3, 3) → B’ (-3, 3)
    C (-1, 2) → C’ (-2, 1)
    Image coordinates of the triangle ABC are A’ (0, 4), B’ (-3, 3) and C’ (-2, 1).

    Find the image coordinates of the triangle ABC, if A (-4, 0), B (-3, 3) and C (-1, 2), which is reflected along y = -x.

    MathematicsGrade9

    If (a, b) is reflected in the line y = -x, its image is the point (-b, -a).
    (a, b) → (-b, -a)
    A (-4, 0)  → A’ (0, 4)
    B (-3, 3) → B’ (-3, 3)
    C (-1, 2) → C’ (-2, 1)
    Image coordinates of the triangle ABC are A’ (0, 4), B’ (-3, 3) and C’ (-2, 1).

    parallel
    Grade9
    Mathematics

    Find the image coordinates of the line AB, if A (3, 2) and B (5, 2), which is reflected along y -axis.

    If (a, b) is reflected in the y-axis, its image is the point (-a, b).
    A (3, 2) → A’ (-3, 2)
    B (5, 2) → B’ (-5, 2)
    Image of the line A’ (-3, 2), B’ ( -5, 2)

    Find the image coordinates of the line AB, if A (3, 2) and B (5, 2), which is reflected along y -axis.

    MathematicsGrade9

    If (a, b) is reflected in the y-axis, its image is the point (-a, b).
    A (3, 2) → A’ (-3, 2)
    B (5, 2) → B’ (-5, 2)
    Image of the line A’ (-3, 2), B’ ( -5, 2)

    Grade9
    Mathematics

    Graph the reflection of the polygon in the given line: y = -3

    Point A is 1 unit below the line, so its reflection is 1 unit above the line at A’ (-6, -2).
    Point B is 2 units above the line, so its reflection is 2 units below the line at B’ (-5, -5).
    Point C is 1 unit above the line, so its reflection is 1 unit below the line at C’ (-3, -4).

    Graph the reflection of the polygon in the given line: y = -3

    MathematicsGrade9

    Point A is 1 unit below the line, so its reflection is 1 unit above the line at A’ (-6, -2).
    Point B is 2 units above the line, so its reflection is 2 units below the line at B’ (-5, -5).
    Point C is 1 unit above the line, so its reflection is 1 unit below the line at C’ (-3, -4).

    Grade9
    Mathematics

    The vertices of a triangle are A (2,3), B (6,1) and C  (7,5). Graph the reflection of the triangle ABC in the given line y-axis.

    Point A is 2 units to the right of the line, so its reflection is 2 units to the left of the line at A’ (-2,3).
    Point B is 6 units to the right of the line, so its reflection is 6 units to the left of the line at B’ (-6,1).
    Point C is 7 units to the right of the line, so its reflection is 7 units to the left of the line at C’ (-7, 5).

    The vertices of a triangle are A (2,3), B (6,1) and C  (7,5). Graph the reflection of the triangle ABC in the given line y-axis.

    MathematicsGrade9

    Point A is 2 units to the right of the line, so its reflection is 2 units to the left of the line at A’ (-2,3).
    Point B is 6 units to the right of the line, so its reflection is 6 units to the left of the line at B’ (-6,1).
    Point C is 7 units to the right of the line, so its reflection is 7 units to the left of the line at C’ (-7, 5).

    parallel
    Grade9
    Mathematics

    If (a, b) is reflected in the line y = -x, its image is the point ________.

    If (a, b) is reflected in the line y = -x, its image is the point (-b, -a).

    If (a, b) is reflected in the line y = -x, its image is the point ________.

    MathematicsGrade9

    If (a, b) is reflected in the line y = -x, its image is the point (-b, -a).

    Grade9
    Mathematics

    If (a, b) is reflected in the line y = x, its image is the point_________.

    If (a, b) is reflected in the line y = x, its image is the point (b, a).

    If (a, b) is reflected in the line y = x, its image is the point_________.

    MathematicsGrade9

    If (a, b) is reflected in the line y = x, its image is the point (b, a).

    Grade9
    Mathematics

    Graph the image of the triangle ABC, if A (-4,0), B (-3,3) and C (-1,2), which is reflected along y-axis.

    If (a, b) is reflected in the y-axis, its image is the point (-a, b).
    (a, b) → (-a, b)
    A (-4, 0)  → A’ (4, 0)
    B (-3, 3) → B’ (3, 3)
    C (-1, 2) → C’ (1, 2)
    Image coordinates of the triangle ABC are A’ (4, 0), B’ (3, 3) and C’ (1, 2).

    Graph the image of the triangle ABC, if A (-4,0), B (-3,3) and C (-1,2), which is reflected along y-axis.

    MathematicsGrade9

    If (a, b) is reflected in the y-axis, its image is the point (-a, b).
    (a, b) → (-a, b)
    A (-4, 0)  → A’ (4, 0)
    B (-3, 3) → B’ (3, 3)
    C (-1, 2) → C’ (1, 2)
    Image coordinates of the triangle ABC are A’ (4, 0), B’ (3, 3) and C’ (1, 2).

    parallel
    Grade9
    Mathematics

    Find the image coordinates of the triangle ABC, if A (-4, 0), B (-3, 3) and C (-1, 2), which is reflected along y = x.

    If (a, b) is reflected in the line y = x, its image is the point (b, a).
    (a, b) → (b, a)
    A (-4, 0)  → A’ (0, -4)
    B (-3, 3) → B’ (3, -3)
    C (-1, 2) → C’ (2, -1)
    Image coordinates of the triangle ABC are A’ (0, -4), B’ (3, -3) and C’ (2, -1).

    Find the image coordinates of the triangle ABC, if A (-4, 0), B (-3, 3) and C (-1, 2), which is reflected along y = x.

    MathematicsGrade9

    If (a, b) is reflected in the line y = x, its image is the point (b, a).
    (a, b) → (b, a)
    A (-4, 0)  → A’ (0, -4)
    B (-3, 3) → B’ (3, -3)
    C (-1, 2) → C’ (2, -1)
    Image coordinates of the triangle ABC are A’ (0, -4), B’ (3, -3) and C’ (2, -1).

    Grade9
    Mathematics

    Find the image coordinates of the line AB, if A (2,3) and B (2,5), which is reflected along x-axis.

    If (a, b) is reflected in the x-axis, its image is the point (a, -b).
    A (2,3) → A’ (2, -3)
    B (2,5) → B’ (2, -5)
    Image of the points A’ (2, -3), B’ (2, -5)

    Find the image coordinates of the line AB, if A (2,3) and B (2,5), which is reflected along x-axis.

    MathematicsGrade9

    If (a, b) is reflected in the x-axis, its image is the point (a, -b).
    A (2,3) → A’ (2, -3)
    B (2,5) → B’ (2, -5)
    Image of the points A’ (2, -3), B’ (2, -5)

    Grade9
    Mathematics

    Graph the reflection of the polygon in the given line: x= -1

    Point A is 5 units to the left of the line, so its reflection is 5 units to the right of the line at A’ (4, -4).
    Point B is 4 units to the left of the line, so its reflection is 4 units to the right of the line at B’ (3, -1).
    Point C is 2 units to the left of the line, so its reflection is 2 units to the right of the line at C’ (1, -2).
    >>>Plot the points to obtain the graph.

    Graph the reflection of the polygon in the given line: x= -1

    MathematicsGrade9

    Point A is 5 units to the left of the line, so its reflection is 5 units to the right of the line at A’ (4, -4).
    Point B is 4 units to the left of the line, so its reflection is 4 units to the right of the line at B’ (3, -1).
    Point C is 2 units to the left of the line, so its reflection is 2 units to the right of the line at C’ (1, -2).
    >>>Plot the points to obtain the graph.

    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.