If a,b,c are collinear points a=(3,4),c=(11,10) ab=2.5 then b=
Answers
Answer:
B is (5, 11/2). verify by finding AB and BC.
Step-by-step explanation:
Given points : A = (3, 4) . C(11, 10).
Slope of straight line AC = (10 -4)/(11-3) = 3/4
Let the point B be (p, q).
Given the length of the line segment AB = 2.5.
A, B and C are collinear.
So slope of AB = (q - 4)/(p - 3) = 3/4
So 4 q - 16 = 3 p - 9
4 q = 3 p + 7 ----- (1)
AB² = (q - 4)² + (p - 3)² = 2.5² = 25/4
p² + q² - 8 q - 6p + 75/4 = 0 --- (2)
(Length of segment AC)² = (10 - 4)² + (11 - 3)² = 100
Length AC = 10
AB = 2.5... So BC = 7.5
We need the point B (p, q) which divides the line joining A (3.4) and C( 11, 10) in the ratio = 1 : 3
So p = (1*11+ 3*3)/(1+3) = 5
q = (1*10 + 3 * 4) /(1+3) = 11/2
SO B is (5, 11/2)
We can verify the values by finding AB and BC.
Step-by-step explanation:
answer to your question is 5,11/2