What is the coordinates of the point that divides the line segment joining (2, 3

What is the coordinates of the point that divides the line segment joining (2, 3) and (4, 7) in the ratio 3:1?

What is the coordinates of the point that divides the line segment joining (2, 3) and (4, 7) in the ratio 3:1?

Step 1: Identify the coordinates of the two points. The first point is (2, 3) and the second point is (4, 7).
Step 2: Understand the ratio in which the line segment is divided. The ratio is 3:1, meaning the first point is weighted more heavily.
Step 3: Use the section formula to find the coordinates of the dividing point. 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.
Step 4: Substitute the values into the formula. Here, m = 3, n = 1, x1 = 2, y1 = 3, x2 = 4, and y2 = 7.
Step 5: Calculate the x-coordinate: P_x = (3*4 + 1*2) / (3 + 1) = (12 + 2) / 4 = 14 / 4 = 3.5.
Step 6: Calculate the y-coordinate: P_y = (3*7 + 1*3) / (3 + 1) = (21 + 3) / 4 = 24 / 4 = 6.
Step 7: Combine the x and y coordinates to get the final point: P = (3.5, 6).

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