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Y_Kistochka [10]
3 years ago
12

The midpoint of \overline{\text{AB}}

Mathematics
1 answer:
Schach [20]3 years ago
4 0

Answer:

<em>The coordinates of b are: B=(-7,-8)</em>

Step-by-step explanation:

We are given the coordinates of the midpoint of \overline{\text{AB}} as M=(-5,-2).

We are also given the coordinates of A=(-3,4). The question requires us to calculate the coordinates of the other endpoint B.

Let (xb,yb) the coordinates of B. The coordinates of the midpoint can be calculated as follows:

\displaystyle x_m=\frac{x_a+x_b}{2}

\displaystyle y_m=\frac{y_a+y_b}{2}

We know xa=-3 and xm=-5. Solve the first equation for xb:

2x_m=x_a+x_b\Rightarrow x_b=2x_m-x_a

Substituting:

x_b=2\cdot (-5)-(-3)=-10+3

x_b=-7

We can solve the second equation for xb and get:

y_b=2y_m-y_a

Since ya=4 and ym=-2, then:

y_b=2\cdot (-2)-(4)=-4-4

y_b=-8

Thus, the coordinates of b are: B=(-7,-8)

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