Question

Given the points A(-1,2) and B(7,6), find the coordinates of the point P on directed line segment AB that partitions the segment into a ratio 1:3. Draw segment AB and plot point P.

a. (1,3)
b. (3,3)
c. (4,5)
d. (9,7)

Answer 1

The coordinates of the point P, which partitions the line segment AB into a ratio of 1:3, are (4,4).

Step-by-step explanation:

To find the coordinates of point P that partitions the line segment AB into a ratio of 1:3, we can use the section formula. The coordinates of point P can be calculated using the formula:

P(x,y) = ((3*A(x) + 1*B(x))/4, (3*A(y) + 1*B(y))/4)

Substituting the values A(-1,2) and B(7,6) into the formula, we get:

P(x,y) = ((3*(-1) + 1*7)/4, (3*2 + 1*6)/4)

This simplifies to:

P(x,y) = (4,4)

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