Question

question 23 (5 points)
dilate the line segment ab with endpoints a(-3,1) and b(4,-2) about the origin with a scale factor 3. find the endpoints of the dilated line segment.
a(0,4), b(7,1)
a(-9,3), b(12,-6)
a(-3,1), b(12,-6)
a(-9,3), b(4,-2)
question 24 (5 points)
find the value of x.
image of a geometric figure with p=p, q, q, r, r, x, 9, 15, 10
7
6
$\frac{10}{3}$
5

Explanation:

Step1: Dilate point A by scale factor 3

Multiply coordinates of A(-3,1) by 3: $(-3×3, 1×3)=(-9,3)$

Step2: Dilate point B by scale factor 3

Multiply coordinates of B(4,-2) by 3: $(4×3, -2×3)=(12,-6)$

Step1: Identify similar triangles

Triangles with sides x,9 and 10,15 are similar (parallel lines imply AA similarity).

Step2: Set up proportion

$\frac{x}{10}=\frac{9}{15}$

Step3: Solve for x

$x=10×\frac{9}{15}=6$

Answer:

A'(-9,3), B'(12,-6)