If a point P divides the line segment joining A(2, 3) and B(8, 7) in the ratio 1

If a point P divides the line segment joining A(2, 3) and B(8, 7) in the ratio 1:3, what are the coordinates of point P?

If a point P divides the line segment joining A(2, 3) and B(8, 7) in the ratio 1:3, what are the coordinates of point P?

Step 1: Identify the coordinates of points A and B. A is (2, 3) and B is (8, 7).
Step 2: Identify the ratio in which point P divides the line segment. 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 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*8 + 3*2)/(1+3)).
Step 6: Calculate the x-coordinate: P_x = (8 + 6) / 4 = 14 / 4 = 3.5.
Step 7: For the y-coordinate: 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 point P. So, P = (3.5, 4).

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