Question

If the mid-point of the line segment joining the points
P(4, 6) and Q(k, 8) is A(x, y) and x + y − 21 = 0, then
the value of k is equal to​

Answer 1

the value of k is 3

hope it helps you ✌

Answer 2

The midpoint of a line segment is joining the points A(c,d) and B(m,n) is $(\frac{c+m}{2},\frac{d+n}{2})$

The coordinates of the midpoint of the line segment joining the points

P(4, 6) and Q(k, 8) is A(x, y).

Calculate the mid point joining the points P(4, 6) and Q(k, 8)

$(\frac{4+k}{2},\frac{6+8}{2})$

Hence, $(\frac{4+k}{2},7)=(x,y)$

$x=\frac{4+k}{2}\\y=7$

Subsitute the value of x and y in equation $x+y-21=0$

$\frac{4+k}{2}+7-21=0\\\frac{4+k}{2}-14=0\\\frac{4+k}{2}=14\\4+k=28\\k=28-4\\k=24$