What is the coordinates of the point that divides the line segment joining (6, 8

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Question: What is the coordinates of the point that divides the line segment joining (6, 8) and (10, 12) in the ratio 1:3?

Options:

Correct Answer: (8, 10)

Solution:

Using the section formula: C = ((1*10 + 3*6)/(1+3), (1*12 + 3*8)/(1+3)) = (8, 10).

What is the coordinates of the point that divides the line segment joining (6, 8) and (10, 12) in the ratio 1:3?

What is the coordinates of the point that divides the line segment joining (6, 8) and (10, 12) in the ratio 1:3?

Step 1: Identify the two points given: Point A is (6, 8) and Point B is (10, 12).
Step 2: Understand that we need to find a point C that divides the line segment AB in the ratio 1:3.
Step 3: Use the section formula, which is: C = ((m*x2 + n*x1)/(m+n), (m*y2 + n*y1)/(m+n)), where m:n is the ratio.
Step 4: In our case, m = 1, n = 3, x1 = 6, y1 = 8, x2 = 10, and y2 = 12.
Step 5: Calculate the x-coordinate of point C: Cx = (1*10 + 3*6) / (1 + 3).
Step 6: Calculate Cx: Cx = (10 + 18) / 4 = 28 / 4 = 7.
Step 7: Calculate the y-coordinate of point C: Cy = (1*12 + 3*8) / (1 + 3).
Step 8: Calculate Cy: Cy = (12 + 24) / 4 = 36 / 4 = 9.
Step 9: Combine the x and y coordinates to get the coordinates of point C: C = (7, 9).

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.