Question

find the coordinates of the vertices after a dilation with a scale factor of 2, centered at the origin.

Explanation:

Step1: Recall Dilation Rule

For a dilation centered at the origin with scale factor \( k \), the coordinates \((x,y)\) transform to \((kx,ky)\).

Step2: Dilate Point A(-3, -5)

Scale factor \( k = 2 \). So, \( x' = -3\times2 = -6 \), \( y' = -5\times2 = -10 \). Thus, A becomes \((-6, -10)\).

Step3: Dilate Point B(-1, 0)

\( x' = -1\times2 = -2 \), \( y' = 0\times2 = 0 \). Thus, B becomes \((-2, 0)\).

Step4: Dilate Point C(3, 5)

\( x' = 3\times2 = 6 \)? Wait, no, original C? Wait, looking at the diagram, maybe C is (3,5)? Wait, the given C is (-3,5)? Wait, the problem's A is (-3,-5), C should be (3,5) for symmetry? Wait, no, the given C is (-3,5)? Wait, the user's diagram: A(-3,-5), B(-1,0), C(-3,5)? No, that can't be. Wait, maybe the original points: Let's check the dilation. Wait, the drop options: for A(-3,-5), scale factor 2: (-6,-10). For B(-1,0): (-2,0). For C(3,5) would be (6,10), but the drop options have (-6,10)? Wait, maybe C is (-3,5). Then \( x' = -3\times2 = -6 \), \( y' = 5\times2 = 10 \). So C becomes (-6,10). For D(-4,0): \( x' = -4\times2 = -8 \), \( y' = 0\times2 = 0 \). So D becomes (-8,0).

Wait, let's match:

• A(-3, -5) → (-6, -10) (matches the drop option (-6, -10))
• B(-1, 0) → (-2, 0) (matches (-2, 0))
• C(-3, 5) → (-6, 10) (matches (-6, 10))
• D(-4, 0) → (-8, 0) (matches (-8, 0))

So the connections are:

A(-3, -5) ↔ (-6, -10)

B(-1, 0) ↔ (-2, 0)

C(-3, 5) ↔ (-6, 10)

D(-4, 0) ↔ (-8, 0)

Answer:

• A(-3, -5) connects to (-6, -10)
• B(-1, 0) connects to (-2, 0)
• C(-3, 5) connects to (-6, 10)
• D(-4, 0) connects to (-8, 0)