If point C is at (2, 3) and point D is at (10, 7), what is the coordinates of po

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Question: If point C is at (2, 3) and point D is at (10, 7), what is the coordinates of point E that divides CD in the ratio 1:3?

Options:

Correct Answer: (5, 4)

Solution:

Using the section formula: E = ((1*10 + 3*2)/(1+3), (1*7 + 3*3)/(1+3)) = (5, 4).

If point C is at (2, 3) and point D is at (10, 7), what is the coordinates of point E that divides CD in the ratio 1:3?

If point C is at (2, 3) and point D is at (10, 7), what is the coordinates of point E that divides CD in the ratio 1:3?

Step 1: Identify the coordinates of points C and D. Point C is at (2, 3) and point D is at (10, 7).
Step 2: Understand that we need to find point E that divides the line segment CD in the ratio 1:3.
Step 3: Use the section formula, which is: E = ((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 = 2, y1 = 3, x2 = 10, y2 = 7.
Step 5: Calculate the x-coordinate of point E: E_x = (1*10 + 3*2) / (1 + 3) = (10 + 6) / 4 = 16 / 4 = 4.
Step 6: Calculate the y-coordinate of point E: E_y = (1*7 + 3*3) / (1 + 3) = (7 + 9) / 4 = 16 / 4 = 4.
Step 7: Combine the x and y coordinates to find point E: E = (4, 4).

Section Formula – The section formula is used to find the coordinates of a point that divides a line segment into a specific ratio.
Coordinate Geometry – Understanding how to work with coordinates in a Cartesian plane and apply geometric concepts.