If point D divides the segment AB with A(2, 3) and B(8, 7) in the ratio 2:3, wha

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Question: If point D divides the segment AB with A(2, 3) and B(8, 7) in the ratio 2:3, what are the coordinates of D?

Options:

Correct Answer: (4.8, 5.2)

Solution:

Using the section formula: D = ((2*8 + 3*2)/(2+3), (2*7 + 3*3)/(2+3)) = (4.8, 5.2).

If point D divides the segment AB with A(2, 3) and B(8, 7) in the ratio 2:3, what are the coordinates of D?

If point D divides the segment AB with A(2, 3) and B(8, 7) in the ratio 2:3, what are the coordinates of D?

Step 1: Identify the coordinates of points A and B. A is at (2, 3) and B is at (8, 7).
Step 2: Understand that point D divides the line segment AB in the ratio 2:3. This means that for every 2 parts from A to D, there are 3 parts from D to B.
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 A, and (x2, y2) are the coordinates of B.
Step 4: Substitute the values into the formula. Here, m = 2, n = 3, (x1, y1) = (2, 3), and (x2, y2) = (8, 7).
Step 5: Calculate the x-coordinate of D: (2*8 + 3*2)/(2+3) = (16 + 6)/5 = 22/5 = 4.4.
Step 6: Calculate the y-coordinate of D: (2*7 + 3*3)/(2+3) = (14 + 9)/5 = 23/5 = 4.6.
Step 7: Combine the x and y coordinates to find D. So, D = (4.4, 4.6).

Section Formula – The section formula is used to find the coordinates of a point that divides a line segment into a given ratio.
Ratio Division – Understanding how to apply the ratio to the coordinates of the endpoints to find the coordinates of the dividing point.