Question

What are the cordinates of the point on the directed line segment from -3 -9 to 4 5 that partitions the segment into a ratio of 5 to 2

Answer 1

Answer:

$(x,y) = (2,1)$

Step-by-step explanation:

Given

Coordinate: (-3,-9) and (4,5)

Ratio= 5 : 2

Required

Determine the point at the segment

The coordinate of the point is calculated using:

$(x,y) = [\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n}]$

Where:

$m : n=5:2$

$(x_1,y_1) = (-3,-9)$

$(x_2,y_2) = (4,5)$

So, we have:

$(x,y) = [\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n}]$

$(x,y) = [\frac{5 * 4 + 2 * -3}{5+2},\frac{5*5+2*-9}{5+2}]$

$(x,y) = [\frac{14}{7},\frac{7}{7}]$

$(x,y) = (2,1)$

The coordinate of the point is: (2,1)