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. What are the coordinates of point p?

Answer 1

The coordinates of point P that partitions the line segment AB in a 1:5 ratio are (-22/3, 23/6). We find these by utilizing the formula for the internal division of a line segment and applying the given endpoints and ratio.

Step-by-step explanation:

To find the coordinates of point P that partitions line segment AB with endpoints A(-9, 3) and B(1, 8) in a 1:5 ratio, we use the formula for internal division of a line segment:

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

Here, m:n is the given ratio, x1, y1 are the coordinates of A, and x2, y2 are the coordinates of B. In this case, A(-9, 3) and B(1, 8) give us:

x1 = -9, y1 = 3, x2 = 1, y2 = 8, and m:n = 1:5.

So, P(x, y) = [(5*(-9) + 1*1)/(5+1), (5*3 + 1*8)/(5+1)]

P(x, y) = [(-45 + 1)/6, (15 + 8)/6]

P(x, y) = [-44/6, 23/6]

P(x, y) = [-22/3, 23/6]

The coordinates of point P are (-22/3, 23/6).