If point C is at (3, 5) and point D is at (9, 1), what is the coordinates of the

If point C is at (3, 5) and point D is at (9, 1), what is the coordinates of the point that divides CD in the ratio 2:3?

If point C is at (3, 5) and point D is at (9, 1), what is the coordinates of the point that divides CD in the ratio 2:3?

Step 1: Identify the coordinates of points C and D. Point C is at (3, 5) and point D is at (9, 1).
Step 2: Understand that we need to divide the line segment CD in the ratio 2:3. This means that for every 2 parts from C, there are 3 parts to D.
Step 3: Use the section formula to find the coordinates of the point that divides the segment. The formula is P = ((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 C, and (x2, y2) are the coordinates of point D.
Step 4: Substitute the values into the formula. Here, m = 2, n = 3, (x1, y1) = (3, 5), and (x2, y2) = (9, 1).
Step 5: Calculate the x-coordinate: P_x = (2*9 + 3*3) / (2+3) = (18 + 9) / 5 = 27 / 5 = 5.4.
Step 6: Calculate the y-coordinate: P_y = (2*1 + 3*5) / (2+3) = (2 + 15) / 5 = 17 / 5 = 3.4.
Step 7: Combine the x and y coordinates to get the final point: P = (5.4, 3.4).

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 formulas related to points.
Ratios – Knowledge of how to apply ratios in dividing segments and understanding their implications in coordinate calculations.