find the coordinates of point x that lies along the directed line segment from Y(-8,8) to T(-15,-13) and partitions the segment in the ratio of 5:2

Question

A. (-5,-15)

B.(-13,-7)

C. (-11.5, -2.5)

D.(-23,-5)

Answer 1

Hi Yared,

There are a couple ways to solve this problem. Likely the easiest is to create the right triangle with the 3rd vertex being the point (-8,-13). Now consider a line parallel to the line joining (-15,-13) and (-8,-13) and intersecting the other two sides of the triangle. That line cuts the other two sides of the triangle into proportional pieces. For the vertical side of the triangle joining (-8,8) with (-8,-13) the ratio between the pieces will be the same as the ratio between the segments of the hypotenuse (5:2). The length of the long leg of the triangle is 8 - (-13) = 21. So we have the equation 5x+2x = 21 giving x = 3. This means the long segment is 5(3)= 15 and short segment is 2(3) = 6. The y coordinate of the point where the parallel line crosses the long leg is -7. Now you need to determine the x-coordinate of the point on the hypotenuse where y also is -7. Determine the equation of the line that represents the hypotenuse, let y = -7 and solve for x.

Here is a graph depicting the above:

https://www.desmos.com/calculator/sznqrcpfj2

But try working out the solution before looking at the graph.