Question

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