Find the coordinates of the point that divides the segment joining (2, 3) and (8

Find the coordinates of the point that divides the segment joining (2, 3) and (8, 7) in the ratio 1:3.

Find the coordinates of the point that divides the segment joining (2, 3) and (8, 7) in the ratio 1:3.

Step 1: Identify the coordinates of the two points. The first point is (2, 3) and the second point is (8, 7).
Step 2: Identify the ratio in which the segment is divided. The ratio is 1:3.
Step 3: Assign values to m and n based on the ratio. Here, m = 1 and n = 3.
Step 4: Use the section formula to find the coordinates of the dividing point. 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*8 + 3*2)/(1+3)).
Step 6: Calculate the x-coordinate: P_x = (8 + 6) / 4 = 14 / 4 = 3.5.
Step 7: Now calculate the y-coordinate using the same formula: P_y = ((1*7 + 3*3)/(1+3)).
Step 8: Calculate the y-coordinate: P_y = (7 + 9) / 4 = 16 / 4 = 4.
Step 9: Combine the x and y coordinates to get the final point. The point is (3.5, 4).

Section Formula – The section formula is used to find the coordinates of a point that divides a line segment in a given ratio.
Ratios – Understanding how to apply the given ratio to the coordinates of the endpoints.
Coordinate Geometry – Basic principles of coordinate geometry are applied to find points in a plane.