Question

Rectangle J'K'L'M' shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applied on trapezoid STUV, as shown below:

Rectangle JKLM is drawn on the grid with vertices J at negative 5, 1. K is at negative 5, 6. L is at negative 7, 6. M is at negative 7, 1. Rectangle J prime K prime L prime M prime is drawn with vertices at J prime 4, 4. K prime is at 4, 9. L prime is at 2, 9. M prime is at 2, 4. Trapezoid STUV is drawn with vertices at S is at 9, negative 6. T is at 9, negative 2. U is at 7, negative 2. V is at 6, negative 5.

What will be the location of U' in the image trapezoid S'T'U'V'?

(16, −2)
(14, −2)
(14, 1)
(16, 1)

Answer 1

(16, 1)

Explanation:

Comparing the pre-image points of JKLM to the image points of J'K'L'M', we see that the x-coordinates increase by 9 and the y-coordinates increase by 3. This is a translation 9 units right and 3 units up.

Applying this same translation to STUV, we will map

U(7, -2) → U'(16, 1).

Answer 2

Location U' in the image trapezoid will be (16, 1)

Explanation:

Rectangle JKLM has been transformed to J'K'L'M'. So changed vertices of JKLM will become as

J(-5,1) → J'(4, 4)

K(5, 6) → K'(4, 9)

L(-7, 6) → L'(2, 9)) Transformation done was shifting of L to L' by (9, 3) [2-(-7)=9, 9-6=3]

M(-7, 1) → M'(2, 4)

Now we have find the find the transformed vertex U' by using the same transformation rule done in L → L'

Since coordinates of U are (7, -2), we will transform is to get get U'

x coordinates = 7 + 9 = 16

y coordinates = -2 + 3 = 1

So U' will be (16, 1).