Question

The right arrow symbol used to show the transition from a point to its image after a transformation is not contained within the Equation Editor. If such a symbol is needed, type "RightArrow." For example: P(0, 0) RightArrow P′(1, 2).
Triangle ABC has coordinates
A (1,4);B(3,−2); and C(4,2).
Find the coordinates of the image
A'B'C' after a reflection over the x-axis.

Answer 1

Given:

Vertices of triangle ABC are A (1,4), B(3,−2) and C(4,2).

Triangle ABC reflected over the x-axis to get the triangle A'B'C'.

To find:

The coordinates of the image A'B'C'.

Solution:

If a figure reflected over the x-axis, then rule of transformation is

$(x,y)\to (x,-y)$

Now, using this rule, we get

$A(1,4)\to A'(1,-4)$

$B(3,-2)\to B'(3,2)$

$C(4,2)\to C'(4,-2)$

Therefore, the coordinates of the image  A'B'C' after a reflection over the x-axis are A'(1,-4), B'(3,2) and C'(4,-2).