Question

If the mid point of the line segment joining the points P(6,a-2)and Q(-2,4) is (2,-4),then find the value of a.

Answer 1

Hope this will help you

Answer 2

Given Question :-

• If the mid-point of the line segment joining the points P (6, a-2) and Q(-2,4) is (2,-4).

To Find :-

• The value of a.

Solution :-

We know to find the midpoint of two ponis say (x1 , y1 ) and (x2 , y2 ) as ;

$\boxed{\boxed{\red{\sf Midpoint=\bigg\lgroup \dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg\rgroup }}}$

Using this formula , we have ,

$=> Midpoint =\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\\=> (2,-4) = \dfrac{6-2}{2},\dfrac{a-2+4}{2}\\=> (2,-4) = 2 , \dfrac{a+2}{2}\\=> -4 =\dfrac{a+2}{2}\\=> (-4)(2)=a-6\\=> -8 = a+2 \\=> a = -2-8\\\bf => a = -10$

$\Large\boxed{\pink{\sf a=(-10) }}$