Question

Triangle ABC with vertices at A(4, 3), B(3, −2), C(−3, 1) is dilated using a scale factor of 1.5 to create triangle A′B′C′. Determine the vertex of point A′.

A′(−6, 4.5)
A′(4, 4.5)
A′(6, 3)
A′(6, 4.5)

Answer 1

To find the vertex of point A' after dilation, we first need to find the coordinates of A′.

We know that when a point is dilated with a scale factor of 1.5, the x-coordinate and y-coordinate are both multiplied by the scale factor.

The coordinates of A are (4, 3).

Multiplying both coordinates by 1.5, we get:
x-coordinate of A′ = 4 * 1.5 = 6
y-coordinate of A′ = 3 * 1.5 = 4.5

Therefore, the vertex of point A′ is A′(6, 4.5).

So the correct option is:
A′(6, 4.5)