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 (6a, 6b), endpoint (3a, 5b)

Accepted Answer

Welcome back. I am so glad you're here. We are told that a line segment has a midpoint at 18 C, 18 D has one end point at seven C 90 and were to determine the coordinates of the other end point. So let's think about this. We've got a midpoint at 18 C D. The 18 C is the X value of our midpoint and the 18 D is the Y value of our midpoint. We also know we have an endpoint, I'll call it endpoint sub one at seven C nine D and we could label the seven C as being the X value for end 70.1 or X sub one and nine D as the Y value for end 90.1 or Y sub one. And what we're trying to find is endpoint two's coordinates, which we don't know what they are, but we could label them for now X sub two and Y sub two. We also know from previous lessons that there is a formula for the midpoint, the midpoint which will be our X sub M Y sub M is equal to the formula X sub one plus, excuse me, X sub one plus X sub two in the numerator divided by two. And why? Sub one plus Y sub two divided by two. And so we can set these equal to each other. We can say X sub M equals X sub one plus X sub 2/2 and Y sub M equals Y sub one plus Y sub 2/2. And now we can fill in what we know for all of those X's and wise. So for the X sub M that is C and it's equal to the X sub one, which is seven C plus our X sub two. That's what we don't know. That's what we're trying to find for that one, all divided by two. And for our wise, we have 18 D equals and in the numerator are Y sub one is nine D, that's plus our unknown Y sub two and that's all over two as well. And now it's just a matter of solving for X two and Y sub two. So let's do that. Taking a look at the X is we are going to multiply everything times to, to cancel out that two in the denominator. So two times 18 C gives us 36 C equal to the twos cancel out on the other side. So we have seven C plus X sub two and X sub two is almost by itself. We can subtract seven C from both sides. 36 C minus seven C equals 29 C. So we have our X sub two. It is 29. That's not it too. It is 29 c. Alright. Now let's solve for R Y sub two again, we'll multiply both sides of the equation times two on the left, 18 D times two is 36 D that equals nine D plus Y step two. On the right hand side, we can subtract both sides by nine D And 36 d -9 d leaves us with 27 d and that's equal to Y sub two. So now we have solved for our wise up to its and we have our endpoints coordinates. So looking at our answer choices for 29 C 27 D that matches with answer choice. C 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 (6a, 6b), endpoint (3a, 5b)

Key Concepts

Midpoint Formula

Coordinate Geometry

Solving for Unknowns

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