Question

staar quiz
8.10(c) - r
name
date
p
1 triangle abc was transformed to create triangle abc 8.10c
which rule best describes this transformation?
a ((x, y)\to(-8x, -2y))
b ((x, y)\to(x + 8, y + 2))
c ((x, y)\to(x - 2, y - 8))
d ((x, y)\to(x - 8, y - 2))

Explanation:

Step1: Identify coordinates of a point

Let's take point \( A \) and \( A' \). Assume \( A \) has coordinates \( (x_1, y_1) \) and \( A' \) has \( (x_2, y_2) \). From the graph, if \( A \) is at \( (2, 1) \) (approximate, need to check grid), \( A' \) is at \( (-6, -1) \). Wait, better to see the horizontal and vertical shifts. Let's find the change in \( x \) and \( y \). Let's take a point, say \( A \): suppose \( A \) is at \( (2, 1) \), \( A' \) is at \( (2 - 8, 1 - 2) = (-6, -1) \). So the change in \( x \) is \( x - 8 \), change in \( y \) is \( y - 2 \). So the transformation rule is \( (x, y) \to (x - 8, y - 2) \), which is option D.

Step2: Verify with another point

Take point \( B \) and \( B' \). If \( B \) is at \( (4, 5) \), \( B' \) should be at \( (4 - 8, 5 - 2) = (-4, 3) \), which matches the graph. Similarly for \( C \), if \( C \) is at \( (3, 3) \), \( C' \) is at \( (3 - 8, 3 - 2) = (-5, 1) \), which also matches. So the rule is \( (x, y) \to (x - 8, y - 2) \), option D.

Answer:

D. \((x, y) \to (x - 8, y - 2)\)