Question

P partitions is in a ratio of 3:2 from R to S. R has coordinates (-2,10), and S has coordinates (3,-5).

What are the coordianes of P?
a. (0.5,2.5)
b. (1,1)
c. (2-2)
d. (-1,7)

Answer 1

Using the section formula for internal division, the coordinates of point P that divides the line segment from R to S in the ratio of 3:2 are calculated to be (1,1).

Step-by-step explanation:

The given problem involves finding the coordinates of point P that divides the segment from point R to point S in the ratio of 3:2. The coordinates of R are (-2,10), and the coordinates of S are (3,-5).

To find the coordinates of P, we can use the section formula, which in the case of internal division is given by:

P(x, y) = [(mx2 + nx1) / (m + n), (my2 + ny1) / (m + n)]

Where x1, y1 are the coordinates of R, x2, y2 are the coordinates of S, and m:n is the given ratio.

Plugging in the values, we get:

P(x, y) = [(3(3) + 2(-2)) / (3 + 2), (3(-5) + 2(10)) / (3 + 2)] = [(9 - 4) / 5, (-15 + 20) / 5]= [5 / 5, 5 / 5] = (1,1)

Therefore, the coordinates of P are (1,1).