Question

Given A(-6, -6) and B(2, 6) find the coordinates of the point P that divides segment AB into the ratio 1:3

Answer 1

The coordinates of point P that divides segment AB in the ratio 1:3 are found using the section formula. By applying the values into the formula, we find that the coordinates of P are (-4, -3).

Step-by-step explanation:

To find the coordinates of the point P that divides the segment AB in the ratio of 1:3, we can use the section formula. The section formula for a line divided in the ratio m:n is given by the coordinates:

X = ​(​(m * x2) + (n * x1)) / (m + n)

Y = ​(​(m * y2) + (n * y1)) / (m + n)

Step-by-Step Application

1. Let the ratio be 1:3. Then, m = 1 and n = 3.
2. Let A(-6, -6) have coordinates (x1, y1) and B(2, 6) have coordinates (x2, y2).
3. Plug in these values into the section formula to get the coordinates of P.
4. X coordinate: X = (​(1 * 2) + (3 * (-6))) / (1 + 3) = (-16) / 4 = -4.
5. Y coordinate: Y = (​(1 * 6) + (3 * (-6))) / (1 + 3) = (-12) / 4 = -3.

Therefore, the coordinates of point P are (-4, -3).