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 (12, 6), endpoint (19, 16)

Accepted Answer

Welcome back. I am so glad you're here. We're told that a line segment has a midpoint at 8 and one endpoint at 25 18. We are to determine the coordinates of the other endpoint. Well, how can we write this? We know that our midpoint is 8 and we could identify our mid points, X and Y values the 10 is the X value for the midpoint or X sub M and the eight is the Y value for the midpoint or Y sub M. Then we have our end point, the first one, I'm going to call that E sub one, that's 25 18 and we could identify again the X and Y values for our endpoint. The 25 is the X value for our end 250.1. So I'll call that X sub one and the 18 is the Y value for our end 180.1. So I'll call that Y sub one. What we're trying to find are the coordinates of E sub two. We don't know what they are yet, but we could call them while we're trying to figure it out. X sub two and Y sub two. What else do we know we know from previous lessons that there is a formula for the midpoint. The midpoint formula is for our X sub M for the X value, we take X sub one plus X sub two and divide that by two. And then for the Y value for R Y sub M for the midpoint, that is why sub one plus Y sub two all over two. And we could set this so that we have X sub M is equal to X sub one plus X sub 2/2. And set our Y sub M equal to Y sub one plus Y sub 2/2. Now we can fill in the X and Y values that we know and solve for X sub two and Y sub two. So our X sub M that is 10, we have 10 equals R X sub one that is 25. So 25 plus our X sub two. That's what we don't know yet. And that's all divided by two. Setting up the wise R Y sub M is eight. That's equal to R Y sub one, which is 18 plus our wise up to which we don't know yet. And that's all divided by two. Now, let's solve for X sub two and Y sub two. I'm going to start off by multiplying both sides of the equation for R X sub two, equation by two to get rid of that two in the denominator on the right hand side, on the left two times 10 is 20 and on the right, the twos cancel out. So we just have 25 plus X sub two, We can subtract 25 from both sides of the equation and 20 minus 25 is negative five. So our X sub two equals negative five, we can fill that in over here. Now let's sulfur are Y sub two. Again, we are going to multiply both sides of the equation by two. So on the left, eight times two is 16 equals on the right, the twos cancel out. So we have 18 plus Y sub two, we can subtract 18 from both sides of the equation. On the left, 16 minus 18 is negative two. So are Y sub two is equal to negative two and that's our end points coordinates. So we want to look for an answer choice that is negative five, negative two that matches with answer choice. A 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 (12, 6), endpoint (19, 16)

Key Concepts

Midpoint Formula

Coordinate Geometry

Solving for Unknowns

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