If point D divides the line segment joining points (2, 5) and (8, 9) in the rati

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Question: If point D divides the line segment joining points (2, 5) and (8, 9) in the ratio 3:1, what are the coordinates of point D?

Options:

Correct Answer: (5, 7)

Solution:

Using the section formula: D = ((3*8 + 1*2)/(3+1), (3*9 + 1*5)/(3+1)) = (5, 7).

If point D divides the line segment joining points (2, 5) and (8, 9) in the ratio 3:1, what are the coordinates of point D?

If point D divides the line segment joining points (2, 5) and (8, 9) in the ratio 3:1, what are the coordinates of point D?

Step 1: Identify the coordinates of the two points. The first point is (2, 5) and the second point is (8, 9).
Step 2: Understand that point D divides the line segment in the ratio 3:1. This means that for every 3 parts from point (2, 5) to point D, there is 1 part from point D to point (8, 9).
Step 3: Use the section formula to find the coordinates of point D. The formula is: D = ((m*x2 + n*x1)/(m+n), (m*y2 + n*y1)/(m+n)), where m and n are the parts of the ratio, (x1, y1) are the coordinates of the first point, and (x2, y2) are the coordinates of the second point.
Step 4: Substitute the values into the formula. Here, m = 3, n = 1, (x1, y1) = (2, 5), and (x2, y2) = (8, 9).
Step 5: Calculate the x-coordinate of point D: D_x = (3*8 + 1*2) / (3+1) = (24 + 2) / 4 = 26 / 4 = 6.5.
Step 6: Calculate the y-coordinate of point D: D_y = (3*9 + 1*5) / (3+1) = (27 + 5) / 4 = 32 / 4 = 8.
Step 7: Combine the x and y coordinates to find point D. The coordinates of point D are (6.5, 8).

Section Formula – The section formula is used to find the coordinates of a point that divides a line segment in a given ratio.