Question
Find point C on the x-axis, so AC + BC is minimum.
A(2, 4), B (6, 2)
- C(4, 0)
- C(4.2, 0)
- C(4.5, 0)
- C(4.7, 0)
Hint:
First plot the points A and B and then obtain image of either A or B and join A and B' or A' and B and point out C on x-axis.
The correct answer is: C(4.7, 0)
* 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.
Given That:
Find point C on the x-axis, so AC + BC is minimum. A(2, 4), B (6, 2)
* We know that A(2, 4), B (6, 2)
* We have to find point C on the x-axis, so AC + BC is minimum.
* First, plot the points in the coordinate system. The shortest distance from point A to point B gives the line that joins these two points.
* Now, reflect point B on the x-axis and locate B’.
* Now, join the line A to B’, the line AB’ intersects at the x-axis at point C.
* This point C is on the x-axis, so AC+ BC is minimum.
* The graph becomes:
>>>Therefore, the required point is C(4,7,0).
The point present in the x-axis. and also on the line image of A and point B.
>>>From the given data the point becomes (4.7,0)
Related Questions to study
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and its image?
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What is the line of reflection for and its image?
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From the graph, the line of reflection is y = x.
What is the line of reflection for and its image?
From the graph, the line of reflection is y = x.
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Find the reflection matrix on the x-axis.
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Write the matrix for the polygon.
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From the graph, the coordinates of polygon are A(0, 2), B(0, 4), C(3, 5), and D(3, 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-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).
Find the image coordinates 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).
Find the image coordinates of the line AB, if A (6, 4) and B (6,1), 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(6, 4) → A’(-4, -6)
B (6,1) → B’(-1, -6)
Image of the line A’( -4, -6), B’( -1, -6)
Find the image coordinates of the line AB, if A (6, 4) and B (6,1), 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(6, 4) → A’(-4, -6)
B (6,1) → B’(-1, -6)
Image of the line A’( -4, -6), B’( -1, -6)
Find the image coordinates of the line AB, if A (6, 4) and B (6, 1), 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 (6, 4) → A’ (4, 6)
B (6, 1) → B’ (1, 6)
Image of line A’ (4, 6), B’ (1, 6)
Find the image coordinates of the line AB, if A (6, 4) and B (6, 1), 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 (6, 4) → A’ (4, 6)
B (6, 1) → B’ (1, 6)
Image of line A’ (4, 6), B’ (1, 6)
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
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
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
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)
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
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 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.
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).
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.
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 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.
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 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.
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).
