Question

Line segment AB has endpoints at A(-9,3) and B(1,8). We want to find the coordinates of point P so that P partitions AB into a part-to-whole ratio of 1:5:

a. P(-3,4)
b. P(-5,6)
c. P(-7,8)
d. P(-1,7)

Answer 1

To find the coordinates of point P that partitions line segment AB into a part-to-whole ratio of 1:5, use the section formula.

Step-by-step explanation:

To find the coordinates of point P that partitions line segment AB into a part-to-whole ratio of 1:5, we can use the section formula. The section formula states that the coordinates of point P, which partitions the line segment AB with endpoints A(x1, y1) and B(x2, y2), in the ratio m:n internally is given by:

P(x, y) = ((n * x1) + (m * x2)) / (m + n), ((n * y1) + (m * y2)) / (m + n)

Using this formula, we can calculate the coordinates of point P for each option. Plugging in the values for m = 1, n = 5, x1 = -9, x2 = 1, y1 = 3, and y2 = 8, we find that:

a. P(-3, 4)

b. P(-5, 6)

c. P(-7, 8)

d. P(-1, 7)

Therefore, the correct answer is d. P(-1, 7).