Question

1. translate rhombus rstu with r(-1, 6), s(3, 7), t(2, 3), and u(-2, 2) under the rule (x, y)→(x + 5, y - 3). what are the coordinates of r?
2. translate triangle xyz with x(-4, 3), y(3, -10) and z(-5, -0) under the rule (x, y)→(x + 2, y - 6). what are the coordinates of y?
3. rotate rectangle cdef with c(-4, 0), d(-1, -0), e(-3, -7) and f(-6, -6) 90° counterclockwise about the origin. what are the coordinates of e?

Explanation:

Step1: Apply translation rule for question 4

For point R(-1, 6) with rule (x, y)→(x + 5, y - 3), calculate new x - coordinate.
$x=-1+5 = 4$

Step2: Calculate new y - coordinate for question 4

$y=6 - 3=3$
So new coordinates of R are (4, 3)

Step3: Apply translation rule for question 5

For point Y(3, - 4) with rule (x, y)→(x + 2, y - 6), calculate new x - coordinate.
$x=3+2 = 5$

Step4: Calculate new y - coordinate for question 5

$y=-4-6=-10$
So new coordinates of Y are (5, - 10)

Step5: Apply 90 - degree counter - clockwise rotation rule for question 6

The rule for a 90 - degree counter - clockwise rotation about the origin is (x, y)→(-y, x). For point E(-3, - 7), new x - coordinate is $x=-(-7)=7$

Step6: Calculate new y - coordinate for question 6

New y - coordinate is $y=-3$
So new coordinates of E are (7, - 3)

Answer:

1. (4, 3)
2. (5, - 10)
3. (7, - 3)