Question

P is the point (-3,4), Q is the point (5,1).
(a) M is the midpoint of PQ
Find the coordinates of M.​

Answer 1

Given the points S(1,6),(1,2) and M(5,2)

M is the mid point of PQ

⇒ Consider the coordinates off Q to be,(x,y)

(

2

1+x

,

2

2+y

)=(5,2)

2

1+x

=5⟹x=9

∴ Coordinates of Q=(9,2)

2

2+y

2⟹y=2

To find the coordinate of R.

distance of SR = distance of QR

⟹

(x−1)

2

+(y−6)

2

=

(x−9)

2

+(y−2)

2

Squaring on both sides,

x 2 _2x+1+y

2

−12y+36=x

2

−18x+81+y

2

−4xy+4

−2x−12y+37=−18x−4y+85

16x−8y−48=0

⟹2x−y−6=0

when x=918−y−6=0

⟹y=12

when y=6,x=6

∴ The coordinates of R =(6,6)

Answer 2

Answer:

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