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Question
The midpoint of the line segment joining A (2a, 4) and B (-2, 3b) is C (1, 2a+1). Find the values of a and b.
Solution
The points are A (2a, 4) and B (-2, 3b).
Let C ( 1,2a + 1) be the mid-point of AB. Then:
` x = (x_1 +x_2) /2 , y = (y_1 +y_2)/2`
` ⇒ 1= (2a (-2))/2 , 2a +1 =(4+3b)/2`
`⇒ 2=2a-2, 4a +2 =4+3b`
⇒2a -2+2, 4a -3b = 4-2
`⇒ a = 4/2 , 4a -3b =2 `
⇒ a =2, 4a -3b =2
Putting the value of a in the equation 4a +3b =2 , we get:
4(2) - 3b =2
⇒ -3b = 2-8=-6
`⇒ b = 6/3 = 2`
Therefore, a =2 and b= 2
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