Find the coordinates of the other endpoint of each line segment, ...

Question

Find the coordinates of the other endpoint of each line segment, given its midpoint and one endpoint. See Example 5(b). midpoint (-9, 8), endpoint (-16, 9)

Accepted Answer

Welcome back. I am so glad you're here. We're told that a line segment has a midpoint at negative 74. It has one end point at negative 24 11 and we need to find the coordinates of the other end point. So let's rewrite this a little bit. We have a midpoint at negative 74. We can think of negative seven as being our X value for the midpoint or X sub M and four as the Y value for our midpoint or Y sub M. We also have our endpoint. I'll call that endpoint one or E sub one and that is negative 24 11. We can think of that as negative 24 being the X value for end 240.1. So X sub one and 11 as the Y value for end 110.1 or why someone and what we're trying to find is endpoint two's coordinates. We don't know what they are yet, but we could label them while we're trying to figure it out as X sub two and Y sub two. What else do we know? We also recall from previous lessons that there's a formula for the midpoint and the midpoint is equal to X sub one plus X sub 2/2. And that's going to be our X coordinate for the midpoint. And then the Y value is going to be Y sub one plus Y sub 2/2. And that is our Y sub M. Well, now we can set up some formulas, we know that our X sub M is equal to our X sub one plus X sub 2/2. And we know that our Y sub M is equal to R Y sub one plus Y sub 2/2. And now we can plug in the excess and wise that we do know. So X sub M that's negative seven and it's equal to X sub one which is negative plus hour. X sub two. That's our unknown that we're trying to find all over to. And now looking at are Y sub M Y sub M is four, that's equal to R Y sub one which is plus the Y sub two. That's our unknown that we're trying to find all divided by two. Now, it's just a matter of solving for X sub two and Y sub two starting with our X sub two, we can multiply both sides of the equation times two and that will be two times negative seven is negative 14. On the left hand side and on the right hand side, the twos cancel out. So this is just negative 24 plus X sub two, we almost have X sub two by itself, we can add 24 to both sides of the equation. And for negative 14 plus 24 that's going to equal positive 10, there's our X sub two. So we can fill that in up here. That's a positive 10. Now, let's solve for Y sub two again, multiplying both sides of the equation by two to get that two on the right hand side to cancel out in the denominator. So four times two is eight that equals the twos cancel out on the right hand side. So it's just 11 plus Y sub two. And why sub two is almost by itself, we can subtract 11 from both sides of the equation eight minus 11 on the left is negative three. So why sub two is negative three? And there is our end points coordinates 10 -3. We look at our answer choices and that matches with answer choice. B well done. We'll catch you on the next one.

Find the coordinates of the other endpoint of each line segment, given its midpoint and one endpoint. See Example 5(b). midpoint (-9, 8), endpoint (-16, 9)

Key Concepts

Midpoint Formula

Coordinate Geometry

Solving for Unknowns

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