The midpoint of AB is M (-2,0). If the coordinates of A are (1,-7) what are the coordinates of B?

Answer 1

Hello, Jameson,

Find the equation of the line that passes through A (1,-7) and M (-2,0). Using the format y = mx + b, calculate the slope, m, by taking the change in y (the "Rise") and dividing by the corresponding change in x (the "run"). Between these two points, we get m = -(7/3).

The equation becomes y = -(7/3)x + b

To find b, use of the the two points and solve for b. We find that b = -(14/3).

The line AB is thus y = -(7/3)x-(14/3).

The point M can be found by using a value for x that is is the same increment for as between A and M, but starting at M. The change in x between A and M is 3 (1 - (-2)) = 3. We need to go to the left of M to find B. M is (-2,0), so we want to find the value of y at point B (-5, ?). Use (-5) for x in the equation to calculate the y coordinate of point B. I get (-5, 7).

It helps to graph the line. There isn't enough room here to post mine.

Bob

Answer 2

Endpoint B (x,y) (missing therefore I called them x and y)

endpoint A (1,-7)

midpoint M (-2,0)

use your midpoint formula:

x₁+x₂ , y₁+y₂

¯¯2¯¯¯ ¯¯2¯¯

(x+1)/2 = -2 (mulitply the 2 on both side )

x+1 = -4 (subtract 1 on both side)

x = -5

(y+-7)/2 = 0 (mulitply the 2 on both side )

y-7 = 0 (add 7 on both side)

y = 7

Endpoint B (-5,7)

Answer 3

Let B(x, y). Then (x + 1)/2 = - 2, (y - 7)/2 = 0. Because x = - 4 - 1 = - 5; y = 0 + 7 = 7. So, B(- 5, 7)