Find the coordinates of the point that divides the line segment joining (1, 2) a

Find the coordinates of the point that divides the line segment joining (1, 2) and (4, 6) in the ratio 1:2.

Find the coordinates of the point that divides the line segment joining (1, 2) and (4, 6) in the ratio 1:2.

Step 1: Identify the coordinates of the two points. The first point is (1, 2) and the second point is (4, 6).
Step 2: Determine the ratio in which the line segment is divided. The ratio given is 1:2.
Step 3: Use the section formula, which 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 the first point, and (x2, y2) are the coordinates of the second point.
Step 4: Substitute the values into the formula. Here, m = 1, n = 2, (x1, y1) = (1, 2), and (x2, y2) = (4, 6).
Step 5: Calculate the x-coordinate: P_x = (1*4 + 2*1) / (1+2) = (4 + 2) / 3 = 6 / 3 = 2.
Step 6: Calculate the y-coordinate: P_y = (1*6 + 2*2) / (1+2) = (6 + 4) / 3 = 10 / 3 = 3.33.
Step 7: Combine the x and y coordinates to get the final point. The coordinates are (2, 3.33).

Section Formula – The section formula is used to find the coordinates of a point that divides a line segment in a given ratio.
Ratio Division – Understanding how to apply the ratio to the coordinates of the endpoints to find the dividing point.