Question

Point P(-10,15) lies on the directed line segment AE. The endpoints are A(-15,1) and E(x,y). What are the coordinates of point E such that AP is 2/5 of the distance from A to E? What is the point of E?

Answer 1

To find the coordinates of point E, use the distance formula to determine the distance between points A and E. Then, apply the ratio AP/AE = 2/5 to find the coordinates of point E. Without the specific values of x and y, the exact coordinates of point E cannot be determined.

Step-by-step explanation:

To find the coordinates of point E, we first need to determine the distance between points A and E. We can use the distance formula, which is:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the coordinates of points A and E:

d = sqrt((x - (-15))^2 + (y - 1)^2)

Next, we know that AP is 2/5 of the distance from A to E. So, we can use the ratio AP/AE = 2/5 to solve for the coordinates of point E.

Let's substitute the coordinates of point P (-10, 15) and the coordinates of point A (-15, 1) into the equation:

2/5 = AP/AE = sqrt((x - (-15))^2 + (y - 1)^2) / sqrt((x - (-15))^2 + (y - 1)^2)

This equation simplifies to:

2/5 = sqrt((x + 15)^2 + (y - 1)^2) / sqrt((x + 15)^2 + (y - 1)^2)

By squaring both sides of the equation, we can eliminate the square roots:

4/25 = (x + 15)^2 + (y - 1)^2 / (x + 15)^2 + (y - 1)^2

The next steps involve simplifying and solving for the coordinates of point E. However, without the values of x and y, we cannot provide the exact coordinates of point E.