If point A is at (1, 2) and point B is at (4, 6), what is the section formula fo

If point A is at (1, 2) and point B is at (4, 6), what is the section formula for point P that divides AB in the ratio 1:2?

If point A is at (1, 2) and point B is at (4, 6), what is the section formula for point P that divides AB in the ratio 1:2?

Step 1: Identify the coordinates of points A and B. Point A is at (1, 2) and point B is at (4, 6).
Step 2: Understand the ratio in which point P divides the line segment AB. The ratio is 1:2.
Step 3: Assign values to m and n based on the ratio. Here, m = 1 and n = 2.
Step 4: Use the section formula for the coordinates of point P. The formula is P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)).
Step 5: Substitute the values into the formula. For the x-coordinate: P_x = ((1*4 + 2*1)/(1+2)).
Step 6: Calculate the x-coordinate: P_x = (4 + 2) / 3 = 6 / 3 = 2.
Step 7: Now calculate the y-coordinate using the same formula: P_y = ((1*6 + 2*2)/(1+2)).
Step 8: Calculate the y-coordinate: P_y = (6 + 4) / 3 = 10 / 3 = 3.33.
Step 9: Combine the x and y coordinates to find point P. Point P is at (2, 3.33).

Section Formula – The section formula is used to find a point that divides a line segment into a specific ratio.
Coordinate Geometry – Understanding the coordinates of points in a Cartesian plane and how to manipulate them.
Ratios – Applying the concept of ratios to determine the relative positions of points along a line segment.