What is the coordinates of the point that divides the line segment joining (2, 3

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Question: What is the coordinates of the point that divides the line segment joining (2, 3) and (4, 7) in the ratio 1:3?

Options:

Correct Answer: (3, 5)

Solution:

Using the section formula: P = ((1*4 + 3*2)/(1+3), (1*7 + 3*3)/(1+3)) = (3, 5).

What is the coordinates of the point that divides the line segment joining (2, 3) and (4, 7) in the ratio 1:3?

What is the coordinates of the point that divides the line segment joining (2, 3) and (4, 7) in the ratio 1:3?

Step 1: Identify the two points given: Point A (2, 3) and Point B (4, 7).
Step 2: Understand the ratio in which the line segment is divided. Here, the ratio is 1:3.
Step 3: Use the section formula, which is: P = ((m*x2 + n*x1)/(m+n), (m*y2 + n*y1)/(m+n)), where m:n is the ratio.
Step 4: Assign values: m = 1, n = 3, x1 = 2, y1 = 3, x2 = 4, y2 = 7.
Step 5: Calculate the x-coordinate using the formula: x = (1*4 + 3*2) / (1 + 3).
Step 6: Calculate: x = (4 + 6) / 4 = 10 / 4 = 2.5.
Step 7: Calculate the y-coordinate using the formula: y = (1*7 + 3*3) / (1 + 3).
Step 8: Calculate: y = (7 + 9) / 4 = 16 / 4 = 4.
Step 9: Combine the x and y coordinates to get the final point: (2.5, 4).

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.