Question

Square RSTU is translated to form R'S'T'U', which has vertices R'(–8, 1), S'(–4, 1), T'(–4, –3), and U'(–8, –3). If point S has coordinates of (3, –5), which point lies on a side of the pre-image, square RSTU?

(–5, –3)
(3, –3)
(–1, –6)
(4, –9)

Answer 1

The point which lies on a side of the pre-image, square RSTU is:

(-1,-6)

Explanation:

We are given that Square RSTU is translated to form R'S'T'U', which has vertices R'(–8, 1), S'(–4, 1), T'(–4, –3), and U'(–8, –3).

Also the vertices of point S are (3,-5).

So let the translation is carried out by the rule:

(x,y) → (x+a,y+b)

That means all the points are translated by the same rule.

We let S(x,y)=(3,-5).

and S'(x,y)=(-4,1)

i.e. (3+a,-5+b)=(-4,1)

i.e. 3+a=-4 and -5+b=1

i.e. a=-7 and b=6

Hence the translation is defined as:

(x,y) → (x-7,y+6)

Hence the pre-image for any point (x',y') will be:

(x'+7,y'-6)

The coordinates of R given that the coordinates of R'(-8,1) is: (-8+7,1-6)=(-1,-5)

Coordinates T are given that coordinates of T'(-4,-3) are: (-4+7,-3-6)=(3,-9)

Coordinates U are given that coordinates of U'(-8,-3) are: (-8+7,-3-6)=(-1,-9)

Hence the vertex of rectangle RSTU are:

R(-1,-5) , S(3,-5) , T(3,-9) and U(-1,-9)

Now we graph this rectangle and also plot the given points in the options and see which point lie on the side of the rectangle RSTU.

The answer is:

(-1,-6)

Answer 2

(–1, –6)

Explanation:

Comparing S to S', we have (3, -5) mapped to (-4, 1). This makes the translation 7 units left and 6 units up; to find the image points from the pre-image points, we subtract 7 from the x-coordinate and add 6 to the y-coordinate.

Working backward from the image points to the pre-image points, we add 7 to the x-coordinate and subtract 6 from the y-coordinate:

R = (-8+7,1-6) = (-1, -5)

T = (-4+7, -3-6) = (3, -9)

U = (-8+7, -3-6) = (-1, -9)

This means that RS goes from (-1, -5) to (3, -5); it means the x-coordinate goes from -1 to 3 and the y-coordinate does not change.

ST goes from (3, -5) to (3, -9); this means that the x-coordinate does not change and the y-coordinate goes from -5 to -9.

TU goes from (3, -9) to (-1, -9); this means the x-coordinate goes from 3 to -1 and the y-coordinate does not change.

UR goes from (-1, -9) to (-1, -5); this means the x-coordinate does not change and the y-coordinate goes from -9 to -5. (-1, -6) will fall along this side.