If point D is at (6, 8) and point E is at (2, 4), what is the section formula ra

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Question: If point D is at (6, 8) and point E is at (2, 4), what is the section formula ratio if point F divides DE in the ratio 1:3?

Options:

Correct Answer: (3, 5)

Solution:

Using the section formula: F = ((1*2 + 3*6)/(1+3), (1*4 + 3*8)/(1+3)) = (5, 7).

If point D is at (6, 8) and point E is at (2, 4), what is the section formula ratio if point F divides DE in the ratio 1:3?

If point D is at (6, 8) and point E is at (2, 4), what is the section formula ratio if point F divides DE in the ratio 1:3?

Step 1: Identify the coordinates of points D and E. Point D is at (6, 8) and point E is at (2, 4).
Step 2: Understand that point F divides the line segment DE in the ratio 1:3. This means that for every 1 part of DE that F is from E, there are 3 parts from D.
Step 3: Use the section formula to find the coordinates of point F. The formula is: F = ((m*x2 + n*x1)/(m+n), (m*y2 + n*y1)/(m+n)), where m and n are the parts of the ratio, (x1, y1) are the coordinates of point E, and (x2, y2) are the coordinates of point D.
Step 4: Substitute the values into the formula. Here, m = 1, n = 3, (x1, y1) = (2, 4), and (x2, y2) = (6, 8).
Step 5: Calculate the x-coordinate of F: F_x = (1*2 + 3*6) / (1+3) = (2 + 18) / 4 = 20 / 4 = 5.
Step 6: Calculate the y-coordinate of F: F_y = (1*4 + 3*8) / (1+3) = (4 + 24) / 4 = 28 / 4 = 7.
Step 7: Combine the x and y coordinates to find point F. Therefore, F = (5, 7).

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 points in a Cartesian coordinate system.
Ratios – Applying the concept of ratios to determine the relative positions of points along a line segment.