A triangle has vertices P(7,7), Q(-3,-5), and R(5,-3).

Question

a. calculate the lengths of the midsegmaents
b. calculate the lengths of the three side of triangle PQR.
c. compare your answers in a. and b. what do you notice?

Answer 1

P(7 , 7) , Po(2 , 1) , Q(-3 , -5).

Q(-3 , -5) , Qo(1 , -4) , R(5 , -3).

R(5 , -3) , Ro(6 , 2) , P(7 , 7).

a. (PPo)^2 = (2 - 7)^2 + (1 - 7)^2,
= 25 + 36 = 61,
PPo = sqrt(61) = 7.8.

(QQo)^2 = (1 - (-3))^2 + (-4 -(-5))^2,
= 16 + 1 = 17,
QQo = sqrt(17) = 4.1.

(RRo)^2 = (6 - 5)^2 + (2 - (-3))^2,
= 1 + 25 = 26,
RRo = sqrt(26) = 5.1.

b. (PQ)^2 = (-3 -7)^2 + (-5 - 7)^2,
= 100 + 144 = 244,
PQ = sqrt(244) = 15.6.

(QR)^2 = (5 - (-3))^2 + (-3 -(-5))^2,
= 64 + 4 = 68,
QR = sqrt(68) = 8.2.

(RP)^2 = (7 - 5)^2 + (7 - (-3))^2,
= 4 + 100 = 104,
RP = sqrt(104) = 10.2.

Answer 2

The Mid-Point formula was used to calculate Po , Qo , Ro:

Xo = (x1 + x2) /2.
Yo = (y1 + y2) / 2.