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, 4) in the ratio 2:1.

Options:

Correct Answer: (2.67, 3.33)

Solution:

Using the section formula: P(x, y) = ((2*3 + 1*1)/(2+1), (2*4 + 1*2)/(2+1)) = (2.67, 3.33).

Find the coordinates of the point that divides the segment joining (1, 2) and (3, 4) in the ratio 2:1.

Find the coordinates of the point that divides the segment joining (1, 2) and (3, 4) in the ratio 2:1.

Step 1: Identify the coordinates of the two points. The first point is (1, 2) and the second point is (3, 4).
Step 2: Identify the ratio in which the segment is divided. The ratio is 2:1.
Step 3: Use the section formula to find the coordinates of the dividing point. The formula is P(x, y) = ((m*x2 + n*x1)/(m+n), (m*y2 + n*y1)/(m+n)), where m and n are the parts of the ratio.
Step 4: Substitute the values into the formula. Here, m = 2, n = 1, x1 = 1, y1 = 2, x2 = 3, and y2 = 4.
Step 5: Calculate the x-coordinate: (2*3 + 1*1)/(2+1) = (6 + 1)/3 = 7/3 = 2.33.
Step 6: Calculate the y-coordinate: (2*4 + 1*2)/(2+1) = (8 + 2)/3 = 10/3 = 3.33.
Step 7: Combine the x and y coordinates to get the final point: (2.33, 3.33).

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