Question

Given the points A(-2, 4) and B(7, -2), find the coordinates of the point P on directed line segment that partitions AB in the ratio 1:2.

Answer 1

To find the coordinates of the point P that partitions AB in the ratio 1:2, we can use the section formula. The coordinates of point P are (3, 2).

Step-by-step explanation:

To find the coordinates of the point P that partitions AB in the ratio 1:2, we can use the section formula. The section formula states that if a point P(x, y) divides the line segment joining points A(x1, y1) and B(x2, y2) in the ratio m:n, then the coordinates of P can be found using the following formulas:

x = (mx2 + nx1) / (m + n)

y = (my2 + ny1) / (m + n)

Using the given points A(-2, 4) and B(7, -2), and the ratio 1:2, we can substitute the values into the formula:

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

y = (1*(-2) + 2*4) / (1 + 2) = 2

Therefore, the coordinates of point P are (3, 2).

Answer 2

When a line segment with point A with the co-ordinates (x1, y1) and point B with the co-ordinates (x2,y2) is divided into the ratio m:n by a point P, we find the x-coordinate of the point by using the following formula: (mx2+nx1)/m+n and the y-coordinate by using this formula: (ny1+my2)/n+m
x-coordinate of P=[(1x7)+(2x-2)]/1+2=1
y-coordinate of Q=[(2x4)+(1x-2)]/2+1=2
Ans: P=(1,2)