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).