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

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

Options:

Correct Answer: (5, 5)

Solution:

Using the section formula: P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where m=1, n=3. P = ((1*8 + 3*2)/(1+3), (1*7 + 3*3)/(1+3)) = (5, 5).

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.