A point Q divides the segment joining P(1, 1) and R(7, 5) in the ratio 2:1. What

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Question: A point Q divides the segment joining P(1, 1) and R(7, 5) in the ratio 2:1. What are the coordinates of Q?

Options:

Correct Answer: (5, 3)

Solution:

Using the section formula: Q = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where m=2, n=1. Q = ((2*7 + 1*1)/(2+1), (2*5 + 1*1)/(2+1)) = (5, 3).

A point Q divides the segment joining P(1, 1) and R(7, 5) in the ratio 2:1. What are the coordinates of Q?

A point Q divides the segment joining P(1, 1) and R(7, 5) in the ratio 2:1. What are the coordinates of Q?

Correct Answer: (5, 3)

Step 1: Identify the coordinates of points P and R. P is (1, 1) and R is (7, 5).
Step 2: Understand that point Q divides the segment PR in the ratio 2:1. This means that Q is closer to P than to R.
Step 3: Assign values to m and n based on the ratio. Here, m = 2 (the part towards R) and n = 1 (the part towards P).
Step 4: Use the section formula to find the coordinates of Q. The formula is Q = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)).
Step 5: Substitute the values into the formula. For the x-coordinate: Qx = ((2*7 + 1*1)/(2+1)).
Step 6: Calculate the x-coordinate: Qx = (14 + 1) / 3 = 15 / 3 = 5.
Step 7: Now calculate the y-coordinate: Qy = ((2*5 + 1*1)/(2+1)).
Step 8: Calculate the y-coordinate: Qy = (10 + 1) / 3 = 11 / 3 = 3.
Step 9: Combine the x and y coordinates to get the coordinates of Q: Q = (5, 3).

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