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 C 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 C that divides AB in the ratio 1:2?

Step 1: Identify the coordinates of point A and point B. Point A is at (1, 2) and point B is at (4, 6).
Step 2: Understand the ratio in which point C 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 to find the coordinates of point C. The formula is C = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)).
Step 5: Substitute the values into the formula. For the x-coordinate: Cx = ((1*4 + 2*1)/(1+2)).
Step 6: Calculate the x-coordinate: Cx = (4 + 2) / 3 = 6 / 3 = 2.
Step 7: Now calculate the y-coordinate using the same formula: Cy = ((1*6 + 2*2)/(1+2)).
Step 8: Calculate the y-coordinate: Cy = (6 + 4) / 3 = 10 / 3 = 3.33.
Step 9: Combine the x and y coordinates to get the final coordinates of point C. C = (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 how to work with coordinates and apply formulas in a Cartesian plane.
Ratios – Knowledge of how to apply ratios in mathematical calculations.