Question

Triangle O,L,D has vertices at (-2, 1), (2, 6), and (8, -3). Triangle N,E,W represents a dilation of triangle O,L,D. If the vertices of triangle N,E,W are located at (-4/3, 2/3), (4/3, 4), and (16/3, -2), which of the following represents the dilation that transforms triangle O,L,D to triangle N,E,W?

a) (x, y), (2/3, x), (2/3, y)
b) (x, y), (4/9, x), (4/9, y)
c) (x, y), (x + 2/3), (y - 1/3)
d) (x, y), (4/3, x), (4/3, y)

Answer 1

To find the dilation scale factor transforming triangle O,L,D into triangle N,E,W, we divide the coordinates of the vertices of N,E,W by those of O,L,D and find that the scale factor is 2/3 for both x and y coordinates, making option a) the correct answer.

Step-by-step explanation:

The question is asking to find the scale factor of the dilation that transforms triangle O,L,D into triangle N,E,W. To solve this, we can compare the coordinates of the corresponding vertices from the two triangles.

If we look at vertex O from triangle O,L,D, its coordinates are (-2, 1), and the corresponding vertex N from the triangle N,E,W has coordinates (-4/3, 2/3). We simply need to divide the coordinates of N by those of O to find the scale factor.

Let's do the calculation for the x-coordinate:

Scale factor (x-coordinate) = (-4/3) / (-2) = 2/3

Now for the y-coordinate:

Scale factor (y-coordinate) = (2/3) / 1 = 2/3

Since the scale factor for both x and y coordinates is the same 2/3, we have determined that the dilation scale factor for transforming triangle O,L,D into triangle N,E,W is 2/3 for both x and y coordinates.

Comparing with the given options, the correct answer is (x, y) → (2/3 × x, 2/3 × y), which corresponds to option a).