Question

Graph triangle RST with vertices R(3, 7), S(-5, -2), and T(3, -5) and its image after a reflection over x = -3.​

Answer 1

Given:

The vertices of a triangle are R(3, 7), S(-5, -2), and T(3, -5).

To find:

The vertices of the triangle after a reflection over x = -3 and plot the triangle and its image on the graph.

Solution:

If a figure reflected across the line x=a, then

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

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

$(x,y)\to (2a-x,y)$

The triangle after a reflection over x = -3. So, the rule of reflection is

$(x,y)\to (2(-3)-x,y)$

$(x,y)\to (-6-x,y)$

The vertices of triangle after reflection are

$R(3,7)\to R'(-6-3,7)$

$R(3,7)\to R'(-9,7)$

Similarly,

$S(-5,-2)\to S'(-6-(-5),-2)$

$S(-5,-2)\to S'(-6+5,-2)$

$S(-5,-2)\to S'(-1,-2)$

And,

$T(3,-5)\to T'(-6-3,-5)$

$T(3,-5)\to T'(-9,-5)$

Therefore, the vertices of triangle after reflection over x=-3 are R'(-9,7), S'(-1,-2) and T'(-3,-5).