Question

the mid point of a line segment joining (2a,4) and (-2,2b) is (1,2a+1). find the value of b

Answer 1

(2a,4) and (-2,2b)
- midpoint 
(2a-2/2) ,(4+2b/2)
(a-1) and (2+b)
a-1= 1    a=2
2(2)+1 = 4+1 = 5
b=5

Answer 2

Answer:

3

Step-by-step explanation:

A = (2a,4)

B = (-2,2b)

C = (1,2a+1)

C is the midpoint of A and B

Formula : $x=\frac{x_1+x_2}{2} , y = \frac{y_1+y_2}{2}$

$A = (x_1,y_1)=(2a,4)$

$B = (x_2,y_2)=(-2,2b)$

$C = (x,y)=(1,2a+1)$

Substitute the values in the formula :

$1=\frac{2a-2}{2}$ ----1  and $2a+1= \frac{4+2b}{2}$ ----2

$2=2a-2$

$a=2$

Substitute the value of a in 2

$2(2)+1= \frac{4+2b}{2}$

$5= \frac{4+2b}{2}$

$10=4+2b$

$6=2b$

$3=b$

Hence the value of b is 3.