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Question

a segment has a midpoint at (2,-7) and an endpoint at (8,-5). what are the coordinates of the other endpoint

Answer 1

The midpoint of a segment is found perfectly in the middle of the two endpoints (x1,y1) and (x2,y2). To find the midpoint, we are given the equation ((x1+x2)/2,(y1+y2)/2)). In this question, it is given to us that the midpoint is at (2,-7) and one of the endpoints is at (8,-5) with the goal being to find the coordinates of the second endpoint. Using the midpoint equation, we can say that (2,-7) = ((8+x2)/2,(-5+y2)/2)) through substitution of the endpoint (8,-5) in for (x1,y1). From this, we can split this into two parts, finding the x2 and finding the y2. First, to find the x2, we can solve for the x-coordinate first (8+x2)/2 = 2 leading us to get x2=-4. We can then solve for the y-coordinate (-5+y2)/2=-7 leading us to get y2=-9. Therefore, we can say that the other endpoint is at (x2,y2) or (-4,-9)

Answer 2

Hi Angela S

Just use the midpoint formula to solve for the missing coordinates

((x₁ + x₂)/2, (y₁ + y₂)/2) = (x_m, y_m)

Where x_m is the x coordinate of the midpoint and y_m is the y coordinate of the midpoint

(x₁ + x₂)/2 = x_m

(y₁ + y₂)/2 = y_m

x_m = 2

y_m = -7

Let the given coordinates from one end serve as (x₁, y₁)

x₁ = 8

y₁ = -5

Now we can plug in the data and solve for the missing parts to get the other end point (x₂, y₂)

(8 + x₂)/2 = 2

8 + x₂ = 2(2)

x₂ = 2(2) - 8

x₂ = 4 - 8 = -4

Same process for y₂

y₂ = 2(-7) - (-5))

y₂ = -14 + 5

y₂ = -9

(x₂, y₂) = (-4, -9)

You can check this by plugging the endpoints into the midpoint formula

(8 +(-4))/2

(8 - 4)/2

4/2 = 2 = x_m

(-5 + -9)/2

(-14)/2

-14/2 = -7 = y_m

I hope this helps