Question

Jill is trying to dilate the triangle on a coordinate plane in reference to the origin using a magnitude of  15 . What are the vertices of the dilated triangle  A′B′C′ ? Enter the number of the correct option.Option #1:  A′(45,1) ,  B′(4,5) ,  C′(6,65) Option #2:  A′(4,54) ,  B′(5,5) ,  C′(6,6) Option #3:  A′(4,1) ,  B′(4,5) ,  C′(6,15)
points (20.25) (4,5) (30,6)

Answer 1

To dilate a triangle on a coordinate plane with respect to the origin, you multiply each vertex of the triangle by the dilation factor.

In this case, Jill is using a dilation factor of 15.

Given the original vertices of the triangle are:
- A(20, 25)
- B(4, 5)
- C(30, 6)

We will calculate the new vertices A', B', and C' by multiplying each coordinate of the original vertices by 15:

1. **For vertex A(20, 25):**
- A' = (20 * 15, 25 * 15) = (300, 375)

2. **For vertex B(4, 5):**
- B' = (4 * 15, 5 * 15) = (60, 75)

3. **For vertex C(30, 6):**
- C' = (30 * 15, 6 * 15) = (450, 90)

Now we have the dilated vertices:
- A' = (300, 375)
- B' = (60, 75)
- C' = (450, 90)

Next, we need to compare these results with the options given.

**Option #1:** A′(45, 1), B′(4, 5), C′(6, 65)
**Option #2:** A′(4, 54), B′(5, 5), C′(6, 6)
**Option #3:** A′(4, 1), B′(4, 5), C′(6, 15)

None of the provided options match the calculated dilated vertices of A'(300, 375), B'(60, 75), and C'(450, 90).

Therefore, none of the options given in the question are correct.