Question

What are the coordinates of the point on the directed line segment from (3, 3) to (7,−5) that partitions the segment into a ratio of 5 to 3

Answer 1

Answer:

The coordinates of the point is (5.5, -2)

Step-by-step explanation:

Okay, what we want to do here is to get the point that divides the line that joins the points (3,3) to (7,-5) in the ratio 5 to 3

Generally, given the ratio a:b and we want to divide the line joining the points (x1,y1) and (x2,y2) in that ratio, we use the condensed formula below;

Let’s call the point dividing the line in the given ratio z.

The coordinates of Z is;

{(bx1 + ax2)/(a+b), (by1 + ay2)/(a+b)}

In this question (x1,y1) = (3,3)

While (x2,y2) = (7,-5)

while a:b = 5:3

Substituting these values into the coordinate equation for point z, we have ;

{((3(3) + 5(7))/(5+3), ((3)(3) + 5(-5))/(5+3)}

= {44/8 , -16/8} = {5.5, -2}