Question

Segment RS is the directed line segment from R(-2,-3) to S(8,2). What are the coordinates of the point that partitions the segment in the ratio 2 to 3?

Point C lies on the directed line segment from A(5,16) to B(-1,2) and partitions the segment in the ratio 1:2. What are the coordinates of C?
Find the coordinate of P, on the coordinate plane, that lies along segment AB and partitions the segment into a 3:2 ratio (AP to PB). Use the following coordinates for the endpoints A(-8,9) and B(2,-6).
Given M(-4,7) and N(12,-1), find the coordinates of point P on segment MN so the P partitions the segment in the ratio 1 to 7 in such a way the MP:PN is 1:7.
The endpoints of segment XY are X(2,-6) and Y(-6,2). What are the coordinates of the point P on segment XY such that XP is 3/4 of the distance from X to Y?

Answer 1

To find the coordinates of a point that partitions a line segment in a certain ratio, use the formula. Plug in the given coordinates and ratios to find the coordinates of the partitioning point.

Step-by-step explanation:

To find the coordinates of a point that partitions a line segment in a certain ratio, we can use the formula:

X = (x1 * m + x2 * n) / (m + n)
Y = (y1 * m + y2 * n) / (m + n)

where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment, and m and n are the ratio values. We can plug in the values from the given coordinates and ratios to find the coordinates of the partitioning point.

• For Segment RS: m = 2, n = 3, x1 = -2, x2 = 8, y1 = -3, y2 = 2
• For Point C: m = 1, n = 2, x1 = 5, x2 = -1, y1 = 16, y2 = 2
• For point P: m = 3, n = 2, x1 = -8, x2 = 2, y1 = 9, y2 = -6
• For point P on segment MN: m = 1, n = 7, x1 = -4, x2 = 12, y1 = 7, y2 = -1
• For point P on segment XY: Let the coordinates of P be (x, y). Since XP is 3/4 of the distance from X to Y, we can find the coordinates using:
  x = 2 + (3/4) * (-6 - 2) = -7
  y = -6 + (3/4) * (2 - (-6)) = -5