Question

question 9 (5 points)
identify the algebraic description that maps a point (3, 7) onto another point (-5, 7).
a) ((x, y) \to (x, y - 8))
b) ((x, y) \to (x + 8, y))
c) ((x, y) \to (x, y + 8))
d) ((x, y) \to (x - 8, y))
question 10 (5 points)
quadrilateral qrst, with vertices q (1, 2), r (3, 4), s (5, 6), and t (2, 7), is dilated by a factor of 2 with the center of dilation at the origin. what are the coordinates of quadrilateral qrst?
a) (q(2, 4), r(10, 12), s(6, 8), t(4, 14))
b) (q(6, 8), r(2, 4), s(10, 12), t(4, 14))
c) (q(2, 4), r(6, 8), s(4, 14), t(6, 8))
d) (q(2, 4), r(6, 8), s(10, 12), t(4, 14))

Explanation:

Question 9 Step1: Compare y-coordinates

The y-coordinate stays 7, so no y change.

Question 9 Step2: Calculate x change

Find difference: $-5 - 3 = -8$. So $x$ becomes $x-8$.

Question 10 Step1: Apply dilation rule

For origin dilation, $(x,y)\to(kx,ky)$ where $k=2$.

Question 10 Step2: Compute each vertex

• $Q'(1\times2, 2\times2)=(2,4)$
• $R'(3\times2, 4\times2)=(6,8)$
• $S'(5\times2, 6\times2)=(10,12)$
• $T'(2\times2, 7\times2)=(4,14)$

Answer:

D) $(x, y) \to (x - 8, y)$
D) $Q'(2, 4), R'(6, 8), S'(10, 12), T'(4, 14)$