The vertices of triangle MNO are M (1,3), N (4,9) and O(7,3). The vertices of triangle PQR are p (3,0), Q (4,2) and R (5,0). Which conclusions is true about the triangles?

(C) They are similar by the definition of similarity in terms of a dilation.

Question:

The complete question as found on wyzant website is stated below:

The vertices of ΔMNO are M (1, 3), N (4, 9), and O (7, 3). The vertices of ΔPQR are P (3, 0), Q (4, 2), and R (5, 0). Which conclusion is true about the triangles?

A). The ratio of their corresponding sides is 1:2.

B).The ratio of their corresponding angles is 1:2.

C).They are similar by the definition of similarity in terms of a dilation.

D).They are congruent by the definition of congruence in terms of rigid motions.

Step-by-step explanation:

To determine which conclusion is true about the triangles, let's graph the coordinates of the points of both triangles.

From the graph, we can see ∆ PQR is similar to ∆MNO with same shape but different sizes.

Both triangles are similar triangles but the ratio of the corresponding sides of ∆MNO to ∆ PQR = 3:1

The image created by a dilation is said to be similar to the original image. The scale factor of a dilation is the ratio of corresponding side lengths, in this case 3:1.

Therefore, they are similar by the definition of similarity in terms of a dilation (C)

for the points

step-by-step explanation:

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