Finding other points on the line given the midpoint

In summary, the student is trying to solve a problem from a textbook that they do not cover in the examples nor have they covered in their assignments. Points P and Q are given but the student does not know how to find the slope of the line to find the midpoint of the two points. They find point R(-11, -23) by taking the difference between the x- and y-coordinates of P and Q.
  • #1
adillhoff
21
0

Homework Statement


Given P(-5, 9) and Q(-8, -7), find a point R such that Q is the midpoint of PR


Homework Equations


[tex]d = \sqrt{(x+8)^2+(y+7)^2}[/tex]


The Attempt at a Solution


Because Q is the midpoint of PR, I know that d(P, Q) = d(Q, R). I also know that d(P, R) = d(Q, R), which is [tex]\sqrt{265}[/tex].

The point of Q is [tex](\frac{-13}{2}, 1)[/tex]. I really don't know where to go from here. This problem is one of the chapter review questions and the book does not cover this specific type of problem in the examples nor did we cover it in our assignments.
 
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  • #2
If Q is the midpoint of PR, per the problem statement, d(P,R) does NOT equal d(Q,R). I'm going to assume that that was a typo, and you meant d(P,Q) = d(Q,R).

I have no idea what you mean, by the point of Q is (-13/2, 1), as point Q is given as (-8,-7).

Since you have two points on a line, there's a couple of ways to go about this. You can determine the slope of the line, and use that to find a point on the other side of Q. Or, you could simply take the difference in the x- and y-coordinates of P&Q and add/subtract them from Q - giving you point R.

First thing you should probably do is graph points P and Q and construct a line, so that you have an idea of about where R should be.
 
  • #3
Yes that was a typo. I also mean to say that the midpoint of PQ = (-13/2, 1). I completely over-analyzed this problem as I do with many problems. I took your advice and found point R(-11, -23) by taking the difference between the x- and y-coordinates of P & Q.

Thanks for your help!
 

1. What is the formula for finding other points on a line given the midpoint?

The formula for finding other points on a line given the midpoint is (x1 + x2)/2 and (y1 + y2)/2, where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line. This will give you the coordinates of the midpoint, and then you can use the distance formula to find the other points on the line.

2. How do you find the distance between the midpoint and the other points on the line?

To find the distance between the midpoint and the other points on the line, you can use the distance formula: √[(x2 - x1)^2 + (y2 - y1)^2], where (x1, y1) is the coordinate of the midpoint and (x2, y2) is the coordinate of the other point. This will give you the length of the line segment between the two points.

3. Can you use the midpoint formula to find other points on a curved line?

No, the midpoint formula is only applicable to straight lines. To find other points on a curved line, you would need to use other mathematical methods, such as calculus or parametric equations.

4. Do you need to know the slope of the line to find other points using the midpoint formula?

No, the midpoint formula does not require you to know the slope of the line. However, knowing the slope can help you determine the direction in which the other points lie on the line.

5. How does finding other points on a line given the midpoint relate to real-world applications?

Finding other points on a line given the midpoint is a useful skill in fields such as engineering, architecture, and physics. It can be used to determine the placement of objects or structures along a line, or to calculate the distance between two points on a map or blueprint. It is also used in computer graphics to draw straight lines between two given points.

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