Point P (5, -3) one of 2 point of trisection of line segment join point A (7, -2) and B (1, -5) near to A. Find the coordinator to the other point of trisection?

Question

Answer

Explanation:

To find the other point of trisection, we need to use the concept of section formula.

Section Formula:
The section formula is used to find the coordinates of a point P which divides the line segment joining two given points A and B internally or externally, in the ratio m:n.

Let the coordinates of point A be (x1, y1) and that of point B be (x2, y2). Let P(x, y) be the point which divides AB in the ratio m:n.

Then the coordinates of P are given by:

x = (mx2 + nx1)/(m + n)
y = (my2 + ny1)/(m + n)

Finding the coordinates of point P:

Given that point A has coordinates (7, -2) and point B has coordinates (1, -5). Let P(x, y) be the point which divides AB in the ratio 1:2.

Using the section formula, we get:

x = (2*1 + 1*7)/(1+2) = 3
y = (2*(-5) + 1*(-2))/(1+2) = -4

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

Finding the coordinates of the other point of trisection:

We know that point P divides AB in the ratio 1:2. Let Q(x, y) be the point which divides PB in the same ratio 1:2.

Using the section formula, we get:

x = (2*3 + 1*5)/(1+2) = 3.33 (approx)
y = (2*(-4) + 1*(-3))/(1+2) = -3.33 (approx)

Hence, the coordinates of the other point of trisection are (3.33, -3.33) (approx).

Therefore, the coordinates of the other point of trisection are (3.33, -3.33) (approx).

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