Mathematics: The vertices of a rectangle are q(−6,2),r(6,2),s(6,−4)q(−6,2),r(6,2),s(6,−4), and t(−6,−4)t(−6,−4). dilate the rectangle with respect to the origin using a scale factor of 3232. then translate it 5 units right and 1 unit down. what are the coordinates of the image?

equal 0Step-by-step explanation:...

The vertices of a rectangle are q(−6,2),r(6,2),s(6,−4)q(−6,2),r(6,2),s(6,−4),

Leslie8284

06.01.2022

The coordinates of the image are Q''(-4,2), R''(14,2), S''(14,-7) and T''(-4,-7).

Step-by-step explanation:

Given information: Q(−6,2),R(6,2),S(6,−4) and T(−6,−4).

If a figure dilated by factor k with respect to the origin , then

$(x,y)\rightarrow (kx,ky)$

The figure dilated with respect to the origin using a scale factor of 3/2.

$(x,y)\rightarrow (\frac{3}{2}x,\frac{3}{2}y)$

The vertices of rectangle after dilation are

$Q(-6,2)\rightarrow Q'(-9,3)$

$R(6,2)\rightarrow R'(9,3)$

$S(6,-4)\rightarrow S'(9,-6)$

$T(-6,-4)\rightarrow T'(-9,-6)$

Then translate it 5 units right and 1 unit down.

$(x,y)\rightarrow (x+5,y-1)$

$Q'(-9,3)\rightarrow Q''(-4,2)$

$R'(9,3)\rightarrow R''(14,2)$

$S'(9,-6)\rightarrow S''(14,-7)$

$T'(-9,-6)\rightarrow T''(-4,-7)$

Therefore the coordinates of the image are Q''(-4,2), R''(14,2), S''(14,-7) and T''(-4,-7).

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