# 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. - Mathematics

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

Concept: Coordinate Geometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 10