If the line segment joining the point (3,-4) and (1,2) is trisected at point p(a,-2) and Q(5/3,b) then
Answers
Given: The line segment joining the point (3,-4) and (1,2) is trisected at point P(a,-2) and Q(5/3,b).
To find: The value of a and b?
Solution:
- Now we have given that the line segment joining the point X(3,-4) and Y(1,2) is trisected at point P(a,-2) and Q(5/3,b).
- So P is the point of trisection of XY.
- That also means P divides XY in 1:2 ratio.
- So by using formula:
mx2 + nx1 / m+n and my2 + ny1 / m+n
P(a,-2) = 2(3) + 1(1) / 1+2 , 2(-4) + 1(2) / 1+2
a , -2 = 7/3 , -2
So a = 7/3
- Similarly Q is the point of trisection of XY.
- That also means P divides XY in 2:1 ratio.
Q(5/3 , b) = 2(1) + 1(3) / 1+2 , 2(2) + 1(-4) / 1+2
5/3 , b = 5/2 , 0
So b = 0
Answer:
So the value of a is 7/3 and b is 0.
Answer:
Given: The line segment joining the point (3,-4) and (1,2) is trisected at point P(a,-2) and Q(5/3,b).
Now,
we have given that the line segment joining the point X(3,-4) and Y(1,2) is trisected at point P(a,-2) and Q(5/3,b).
P is the point of trisection of XY.
That means P divides XY in 1:2 ratio.
By using formula:
mx2 + nx1 / m+n and my2 + ny1 / m+n
P(a,-2) = 2(3) + 1(1) / 1+2 , 2(-4) + 1(2) / 1+2
a , -2 = 7/3 , -2
a = 7/3
=> Similarly Q is the point of trisection of XY.
=> That also means P divides XY in 2:1 ratio.
Q(5/3 , b) = 2(1) + 1(3) / 1+2 , 2(2) + 1(-4) / 1+2
5/3 , b = 5/2 , 0
b = 0
Hence
The value of a is 7/3 and b is 0.