Mathematics
Grade9
Easy

Question

Find point C on the x-axis, so AC + BC is minimum.
A(4, -3), B (8, -5)

  1. (5.5, 0)
  2. (5.4, 0)
  3. (5.3, 0)
  4. (5.2, 0)

hintHint:

Plot the points on the graph and then join either A'B or AB' and take point that intersects with x-axis.

The correct answer is: (5.5, 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 when A(4, -3), B (8, -5).
    * We know that A(4, -3), B (8, -5)
    * 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 A on the x-axis and locate A’.
    * Now, join line A’ to B; line A’B intersects at the x-axis at point C.
    * This point C is on the x-axis, so AC+ BC is minimum.
    >>>The required graph is:

    >>>Therefore, the point on the x-axis that makes AC+BC as minimum is (5.5,0).

    >>>Finding A'B line AB' line intersection point gives the point that gives minimum sum of AC and BC on x-axis.
    >>>Therefore, the point of intersection becomes: C(5.5,0).

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