What are the coordinates of the point on the directed line segment from (-2, -5)(−2,−5) to (7, 10)(7,10) that partitions the segment into a ratio of 2 to 1?

Given:

The directed line segment from (-2, -5) to (7, 10).

A point partitions the segment into a ratio of 2 to 1.

To find:

The coordinates of that point.

Solution:

Section formula: If a point divides a line segment in m:n, then the coordinates of that point are

The point divides the line segment from (-2, -5) to (7, 10) in 2:1.

Using section formula, we get

Therefore, the coordinates of the partition point are (4,5).

your answer is the frist one

hop i

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is