Find the coordinates of the other endpoint of each line segmen...

Question

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

midpoint $open paren 5 comma 8 close paren$ , endpoint $open paren 13 comma 10 close paren$

Accepted Answer

Welcome back. I am so glad you're here. We are told that we have a line segment with a midpoint at 8, 12, 1 endpoint at 15 6 and were to determine the coordinates of the other endpoint. All right. How can we write this? We have a midpoint at 8 12. Well, eight is the X value of our midpoint. We can call that X sub M and then 12 is the Y value of our midpoint. We can call that Y sub M. How about our endpoints? Well, our first one that we know we can call that endpoint one or E sub one that is 15 6 and we can identify our 15 is the X value of the endpoint one. So we can call that X sub one and six is the Y value of our end 60.1. So we can call that Y sub one. What we don't know is endpoint two's coordinates. So we can leave a space for those. But while we're trying to figure it out, we can identify them as X sub two and Y sub two for endpoint to what else do we know? We recall from previous lessons? That there is a formula for the midpoint. The midpoint is, it's got an X sub M value determined by taking X sub one plus X sub two and dividing that all by two. And then it has a Y sub M value that you find by taking Y sub one plus Y sub two, all divided by two. So we could write this as two equations. We could set X sub M equal to X sub one plus X sub 2/2. And we can set our Y sub M equal to Y sub one plus Y sub two all over two. Now we can fill in the excess and wise that we know and solve for X sub two and Y sub two. So let's do that. X sub M that is eight and it is equal to X sub one which is 15 plus our X sub two. That is what we don't know. And that's all over two. Let's set up our Y R Y sub M R Y sub M is are Y sub one is six plus. We don't know our Y sub two yet. That is just Y sub two for now all over too. Now we can solve for X sub two and Y sub two on the left for our X up to I'm going to multiply both sides of the equation times two to get the two to cancel out on the right hand side. And the denominator on the left 16 times, excuse me, eight times two is 16. And on the right, the twos cancel out. So that's 15 plus X sub two, we can subtract 15 from both sides of the equation. On the left 16 minus 15 is one. So one equals X sub two, we can fill that in for our X sub two value. Now let's solve for Y sub two again, multiplying both sides of the equation by two to get the twos to cancel out. On the right hand side where the denominator is two times 12 on the left is 24 equals the twos cancel out. So we have six plus Y sub two. Now we can subtract six from both sides of the equation on the left. 24 minus six is 18 that equals our Y sub two. So Y sub two is positive 18 while we have our endpoints coordinates one and 18, looking at our answer choices that matches with answer choice. A well done, we will 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 $open paren 5 comma 8 close paren$ , endpoint $open paren 13 comma 10 close paren$

Key Concepts

Midpoint Formula

Solving for an Unknown Endpoint

Coordinate Geometry Basics

Watch next