Question

P is the mid-point of line segment AB.

Al lies at (-a, a + 1). P is at (-7,+6), and B is at (-3, a+3).
2
Find the value of a.

Answer 1

Explanation:

the midpoint coordinates of points A and B are

((xa + xb)/2, (ya + yb)/2)

and it is in our case (-7, 6).

if you did not leave anything out

xa = -a

ya = a + 1

xb = -3

yb = a + 3

so,

-7 = (-a + -3)/2 = (-a - 3)/2

6 = ((a + 1) + (a + 3))/2 = (2a + 4)/2 = a + 2

from this second equation we get

6 = a + 2

a = 4

but that does not fit to the first equation.

-7 = (-a - 3)/2

-14 = -a - 3

-11 = -a

a = 11

so, something is wrong with your given information.

the simplest correction would be if B is actually

B = (-10, a+3)

then it all works out for a = 4.