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3 years ago

Find the coordinates of the endpoint A given B (-3,5) is the midpoint of AC and C (1,-2)

Mathematics

1 answer:

WARRIOR [948]3 years ago

6 0

coordinates of endpoint A are (-7,12)

Step-by-step explanation:

We are given midpoint B (x,y) =(-3,5)

One endpoint C (x₂,y₂)= (1,-2)

We need to find other endpoint A (x₁,y₁).

The formula to find midpoint is:

$x=\frac{x_{1}+x_{2}}{2}\\y=\frac{y_{1}+y_{2}}{2}$

We can find the coordinates of endpoint A using these formula.

We have x=-3, x₁=? and x₂= 1

Putting values and finding x₁

$x=\frac{x_{1}+x_{2}}{2}\\-3=\frac{x_{1}+1}{2}\\-6=x_{1}+1\\-6-1=x_{1}\\x_{1}=-7$

Now, y=5, y₁=? and y₂= -2

$y=\frac{y_{1}+y_{2}}{2}\\5=\frac{y_{1}+-2}{2}\\5*2=y_{1}+-2\\10=y_{1}+-2\\10+2=y_{1}\\y_{1}=12$

SO, coordinates of endpoint A are (-7,12)

Keywords: Midpoint of line segment

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