Question

Find the dilation of
3
3 with center
(
0
,

0
)
(0, 0) for the following points if
�
(
−
1
,

2
)
A(−1, 2)
�
(
4
,

5
)
B(4, 5)

Answer 1

To find the dilation of point A(-1, 2) with a center at (0, 0), we can use the formula:

Dilated point = (x - h, y - k) * dilation factor + (h, k)

Given that the center is (0, 0) and the dilation factor is 3, we can substitute these values into the formula:

Dilated point = (-1 - 0, 2 - 0) * 3 + (0, 0)
= (-1, 2) * 3 + (0, 0)
= (-3, 6) + (0, 0)
= (-3, 6)

Therefore, the dilation of point A(-1, 2) with a center at (0, 0) is (-3, 6).

Now, let's find the dilation of point B(4, 5) with the same center and dilation factor:

Dilated point = (x - h, y - k) * dilation factor + (h, k)

Dilated point = (4 - 0, 5 - 0) * 3 + (0, 0)
= (4, 5) * 3 + (0, 0)
= (12, 15) + (0, 0)
= (12, 15)

Therefore, the dilation of point B(4, 5) with a center at (0, 0) is (12, 15).