Answer: (3, -3)
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Step-by-step explanation:
Let's focus on only the x coordinates for now.
The endpoint has x coordinate 6 and the midpoint's x coordinate is 4.5
The other endpoint's x coordinate is unknown. I'll call this P. I'm tempted to use x, but I want to avoid being this repetitious using x.
What happens is that we add up the two endpoint values, and divide by 2, to get the midpoint value. We'll use algebra to solve for P.
So,
midpoint = (endpoint1 + endpoint2)/2
4.5 = (6 + P)/2
4.5*2 = 6+P
9 = 6+P
P = 9-6
P = 3
This mystery endpoint has 3 as its x coordinate.
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Now onto the y coordinate. We'll use the same idea as the last section.
The y coordinates are...
- -2 for the first endpoint
- -2.5 for the midpoint
- Q for the other endpoint, aka some unknown value
So,
(endpoint1 + endpoint2)/2 = midpoint
(-2 + Q)/2 = -2.5
-2+Q = 2(-2.5)
-2+Q = -5
Q = -5 + 2
Q = -3
The y coordinate for the other endpoint is -3
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To wrap everything up, we found that the other endpoint has x and y coordinates of 3 and -3 in that exact order.
Therefore, the missing endpoint is (3, -3)
If you were to apply the midpoint formula on (6,-2) and (3,-3) then you would find the midpoint is (4.5, -2.5). This will help confirm the answer.
Check out the diagram below for visual confirmation. This part is optional but I find it's handy to have. The diagram shows point A in blue as the given endpoint and point C in black as the given midpoint. The red point B is the answer we're after, aka that mystery endpoint.