Find the coordinates of the point that divides the segment joining (1, 2) and (3

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Question: Find the coordinates of the point that divides the segment joining (1, 2) and (3, 8) in the ratio 1:3.

Options:

Correct Answer: (2, 6)

Solution:

Using the section formula: (mx2 + nx1)/(m+n), (my2 + ny1)/(m+n) where m=1, n=3. Coordinates = ((1*3 + 3*1)/(1+3), (1*8 + 3*2)/(1+3)) = (2, 6).

Find the coordinates of the point that divides the segment joining (1, 2) and (3, 8) in the ratio 1:3.

Find the coordinates of the point that divides the segment joining (1, 2) and (3, 8) in the ratio 1:3.

Step 1: Identify the coordinates of the two points. The first point is (1, 2) and the second point is (3, 8).
Step 2: Determine the ratio in which the segment is divided. The ratio given is 1:3.
Step 3: Assign values to m and n based on the ratio. Here, m = 1 and n = 3.
Step 4: Use the section formula to find the x-coordinate of the dividing point. The formula is (mx2 + nx1) / (m+n).
Step 5: Substitute the values into the formula for the x-coordinate: (1*3 + 3*1) / (1+3).
Step 6: Calculate the x-coordinate: (3 + 3) / 4 = 6 / 4 = 1.5.
Step 7: Use the section formula to find the y-coordinate of the dividing point. The formula is (my2 + ny1) / (m+n).
Step 8: Substitute the values into the formula for the y-coordinate: (1*8 + 3*2) / (1+3).
Step 9: Calculate the y-coordinate: (8 + 6) / 4 = 14 / 4 = 3.5.
Step 10: Combine the x and y coordinates to get the final coordinates of the dividing point: (1.5, 3.5).

Section Formula – The section formula is used to find the coordinates of a point that divides a line segment in a given ratio.
Ratios – Understanding how to apply ratios correctly in the context of dividing a segment.