Know How to Use the Mid-Point Formula to Find Missing Coordinates

By Team Aakash Byju's | 6th December 2022

The coordinates of the mid-point of the line joining the points   (3p, 4) and (-2, 2q) are (5, p). Find the values of p and q.

y

x

(3p, 4)

(5, p)

(-2, 2q)

Let A(3p, 4) and B(-2, 2q) be two endpoints and O(5, p) be the midpoint.

(3p, 4)

(-2, 2q)

(5, p)

If (x , y ) and (x  , y  ) are the endpoints, then the mid-point (x,y) is found using the formula

1

1

2

2

(x , y)

=

x  + x

2

y  + y

2

1

2

2

1

(

)

=> x =

,

x  + x

2

1

2

,

y =

y  + y

2

2

1

(x , y )

1

1

2

(x  , y )

(x , y )

2

(3p, 4)

(-2, 2q)

(5, p)

Using the given coordinates in the formula, we get

(5,p) =

3p + -2

2

4 + 2q

2

(

)

,

=> 5 =

3p + (-2)

2

4 + 2q

2

,

p =

(     )

(3p, 4)

(-2, 2q)

(5, p)

Solve equations one by one to find the values of p and q.

5 =

3p +  -2

2

=>10 = 3p-2

10+2 = 3p => p=

12

3

= 4

(     )

(3p, 4)

(-2, 2q)

(5, p)

Use the value of p in the other equation to find the value of q

p =

4 + 2q

2

=>4 =

4 + 2q

2

=> 4 × 2 = 4+2q  =>  8-4= 2q

=> q =

4

2

= 2

Thus, (p,q)=(4,2).