Proof A. B. C. and D.

Question

3. Given: P(1, 2), Q(­3, ­1) and R(1, ­4).

a. Prove that ΔPQR is not equilateral.

b. Find the midpoints of QP and QR and label them M and N respectively.

c. Find the areas of ΔPQR and ΔMQN.

d. What is the ratio of the area of ΔMQN to ΔPQR?

Answer 1

Compute distance between points PQ, QR and PR using distance formula sqrt((x2-x1)^2 + (y2-y1)^2).

For example distance between P and Q is sqrt((3-1)^2 + (1-2)^2) = sqrt(5).

Do prove PQR is not equilateral all 3 distances should not be the same.

Find midpoint of QP and QR using the midpoint formula ((x1 + x2)/2, (y1 + y2) / 2)

For example midpoint of QP is ( (3 + 1)/2, (1 + 2)/2) = (2,1.5).

To find the area of PQR compute the midpoint of PR (label it x) and then compute the distance XQ.

Area will be 1/2 * distance PR * distance XQ.

To find the area of MQN compute the midpoint of MN (label it y) and then compute the distance YQ. Compute the distance between M and N.

Area will be 1/2 * distance MN * YQ.