Question

If T is the centroid of ∡MNP, TN = 16, MQ = 23, and RP = 18, find each missing measure.

a) QT = ______

b) QN = ______

c) QP = ______

d) MP = ______

e) RT = _______

f) TP = ________

Answer 1

a) QT = 8

b) QN = 24

c) QP = 23

d) MP = 46

e) RT = 6

f) TP = 12

Explanation:

Find the diagram attached

If T is the centroid of<MNP, then the following are true;

TN = 2QT

Given TN = 16

16 = 2QT

QT = 16/2

QT = 8

QN = QT + TN

QN = 8 + 16

QN = 24

MQ + QP = MP and MQ = QP

If MQ = 23

QP = 23

Recall that MP = MQ + QP

MP = MQ + MQ

MP = 2MQ

MP = 2(23)

MP = 46

Similarly, TP = 2RT

RT = TP/2

Also RP = RT + TP

RP = RT + 2 RT

RP = 3RT

18 = 3RT

RT = 18/3

RT = 6

Recall that TP = 2RT

TP = 2(6)

TP = 12