Question

The rule R x-axis ∘ T⟨–5, 3⟩ is applied to the point (–3, –2). Where is the image in the coordinate system?

Answer 1

Given:

Rule of transformation is rule R x-axis ∘ T⟨–5, 3⟩.

The point is (-3,-2).

To find:

The image of given point after the transformation.

Solution:

Consider the given point be P(-3,-2).

Rule of transformation is rule R x-axis ∘ T⟨–5, 3⟩. If means first we have apply translation T⟨–5, 3⟩ after that we have to apply reflection R x-axis.

If a figure translated by T⟨–5, 3⟩, then

$(x,y)\to (x-5,y+3)$

$P(-3,-2)\to P'(-3-5,-2+3)$

$P(-3,-2)\to P'(-8,1)$

If a figure reflected by R x-axis, then

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

$P'(-8,1)\to P''(-8,-1)$

Therefore, the image of given point after transformation is (-8,-1).