If point P divides the segment joining (2, 3) and (8, 7) in the ratio 3:1, what
Practice Questions
Q1
If point P divides the segment joining (2, 3) and (8, 7) in the ratio 3:1, what are the coordinates of P?
(5, 4)
(6, 5)
(7, 6)
(4, 5)
Questions & Step-by-Step Solutions
If point P divides the segment joining (2, 3) and (8, 7) in the ratio 3:1, what are the coordinates of P?
Step 1: Identify the coordinates of the two points. The first point is (2, 3) and the second point is (8, 7).
Step 2: Understand the ratio in which point P divides the segment. The ratio is 3:1, meaning P is closer to the point (8, 7).
Step 3: Use the section formula to find the coordinates of point P. 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, (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 = 3, n = 1, (x1, y1) = (2, 3), and (x2, y2) = (8, 7).
Step 5: Calculate the x-coordinate of P: (3*8 + 1*2)/(3+1) = (24 + 2)/4 = 26/4 = 6.
Step 6: Calculate the y-coordinate of P: (3*7 + 1*3)/(3+1) = (21 + 3)/4 = 24/4 = 6.
Step 7: Combine the x and y coordinates to get the coordinates of point P, which are (6, 6).
Section Formula – The section formula is used to find the coordinates of a point that divides a line segment in a given ratio.
