If p divides a line segment AB, A ( 1 , 2) and ( 7,5) in the ratio 1:2 P is ____a.( - 3, 0)b.( -3 , -3)c.( 3, 3)d.( 2, 3)
Question
If p divides a line segment AB, A (1, 2) and (7,5) in the ratio 1:2 P is ____
a. ( -3, 0)
b. ( -3 , -3)
c. ( 3, 3)
d. ( 2, 3)
Solution
The coordinates of a point P(x, y) that divides a line segment AB with coordinates A(x1, y1) and B(x2, y2) in the ratio m:n is given by the formula:
x = (mx2 + nx1) / (m + n) y = (my2 + ny1) / (m + n)
Here, the points are A(1, 2) and B(7, 5). So, x1 = 1, y1 = 2, x2 = 7, and y2 = 5. The ratio is 1:2, so m = 1 and n = 2.
Substitute these values into the formula:
x = (17 + 21) / (1 + 2) = (7 + 2) / 3 = 9 / 3 = 3 y = (15 + 22) / (1 + 2) = (5 + 4) / 3 = 9 / 3 = 3
So, the point P that divides the line segment AB in the ratio 1:2 is P(3, 3).
Therefore, the correct answer is c. (3, 3).
Similar Questions
One of the two points of trisection of the line segment joining the points A(7, –2) and B(1, –5) which divides the line in the ratio 1 : 2 is :
The point which divides the line segment joining the points (7, -6) and (3, 4) in ratio 1 : 2 internally lies in the
What is the ratio in which the line segment joining (2,-3) and (5, 6) is divided by x-axis?(a) 1:2 (b) 2:1 (c) 2:5 (d) 5:2
If the point P (2, 1) lies on the line segment joining points A (4, 2) and B (8, 4),then(A) AP = 13 AB (B) AP = PB (C) PB = 13 AB (D) AP = 12 AB
What is the midpoint of a line segment with the endpoints (-6, -3) and (9, -7)?A.(-4.5, 1)B.(1.5, -5)C.(-5, 1.5)D.(1, -4.5)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.