SOLUTION: pls help me... Given the points P(-1,-2) Q(4,2) and R(1,m) in the coordinate plane. Find the value of m so that PR + RQ is minimum...thanks

Question 118439: pls help me...
Given the points P(-1,-2) Q(4,2) and R(1,m) in the coordinate plane. Find the value of m so that PR + RQ is minimum...thanks
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Plot the points P and Q on a graph. Then construct the vertical line x = 1. R can then be any point on that vertical line.

If R is any point that is NOT on line PQ, then PQR forms a triangle and PR + RQ > PQ. But, if R is colinear with P and Q, then PR + RQ = PQ. Lastly, there is no possible value for m that would create a situation where PR + RQ < PQ. Therefore, the minimum value for m is the point where R is colinear with P and Q.

Now all you have to do is find the equation for the line containing P and Q and evaluate it at x = 1 to find your value for m. I assume that you know the two-point form of a straight line, and leave the rest to you. If you are still having trouble, write back and we'll work it out.

Hope that helps,
John
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