Midpoints of sides PQ(-2,3) QR(5,-1) PR(-4,-7) . Find the coordinates of P, Q, and R

Question

Math problem year 10, geomatry coordinates

Answer 1

triangle PQR with midpoints (-2,3), (5,-1), and (-4,-7)

P=(a,b), Q=(c,d), R=(e,f)

working with the x-coordinates first...

segment PQ:

(a+c)/2=-2

segment QR:

(c+e)/2=5

segment RP:

(e+a)/2=-4

a+c=-4

c+e=10

e+a=-8 -------->e=-a-8

a+c=-4

c+(-a-8)=10

c-a=18

c+a=-4

2c=14

c=7

a=-11

e=3

now work with the y-coordinates in the same manner

(b+d)/2=3

(d+f)/2=-1

(f+b)/2=-7

b+d=6

d+f=-2------>f=-2-d

f+b=-14

-2-d+b=-14

-d+b=-12

d+b=6

2b=-6

b=-3

d=9

f=-11

P=(-11,-3), Q=(7,9), R=(3<-11)

 

 

 

 

Answer 2

You could use the centroid and sketch it out.