Question

Find the value of k if p(4,-2) is the midpoint of the line segment joining the point A. (5k,3)and B(-k,-7)

Answer 1

Recall your method of finding the midpoint:

For the x of the midpoint, add the x values of the endpoints, then divide by 2 (in effect you are taking the average of the x's)
For the y of the midpoint .... (same thing)

let's check if they did the y value correctly.
( 3 + (-7))/2
= -4/2
= -2
yup, that's what they have as the midpoint y value

now repeat for the x value, and find k

let me know what you got.

Answer 2

Let the point p[4,-2] =[x1,y1]
a[....] =[x2,y2]
B[....] =[x3,y3]
Now put the value in this formula,

1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]=O

Your answer will be 2. I mean value of k will be 2