Question

Given the points C(-2, 4) and D(7, -2), find the coordinates of the point P that is one-third of the distance from C to D.

A) (1, 2)
B) (2, 0)
C) (3, 1)
D) (4, -1)

Answer 1

To find the coordinates of point P that lies one-third of the distance from C to D, calculate the changes in x and y coordinates, divide them by three, and add these values to the coordinates of C. The result gives the coordinates of point P as (1, 2), which is option A) (1, 2).

Step-by-step explanation:

To find the coordinates of point P that is one-third of the distance from C to D, we start with the coordinates of C(-2, 4) and D(7, -2). We need to compute the change in x-coordinate (Δx) and the change in y-coordinate (Δy) between C and D.

Δx = Dx - Cx = 7 - (-2) = 9
Δy = Dy - Cy = -2 - 4 = -6

Now, we find one-third of these changes because P is one-third of the distance from C to D:

• ΔxP = Δx / 3 = 9 / 3 = 3
• ΔyP = Δy / 3 = -6 / 3 = -2

Next, we add these changes to the coordinates of C to find the coordinates of P:

• Px = Cx + ΔxP = -2 + 3 = 1
• Py = Cy + ΔyP = 4 + (-2) = 2

Thus, the coordinates of point P are (1, 2), which corresponds to option A) (1, 2).