Question

p( -2,5) q(3,2) are two points. find the co-ordinates of the point R on pq such that PR=2QR​

Answer 1

Given :- P( -2,5) Q(3,2) are two points. find the co-ordinates of the point R on pq such that PR = 2QR ?

Solution :-

given that,

→ PR = 2 * QR

So,

→ PR / QR = 2 / 1 .

→ PR : QR = 2 : 1.

Now, we know that, section formula says that, if R(x,y) divides P(a, b) and Q(c, d) in ratio m : n , than :-

• P(x , y) = (cm + an)/(m + n) , (dm + bn)/(m + n) .

from question we have :-

• P(a, b) = (-2, 5)
• Q(c, d) = (3 , 2)
• m : n = 2 : 1

Putting all values we get :-

→ x = (cm + an)/(m + n)

→ x = (3 * 2 + (-2)*1) / (2 + 1)

→ x = (6 - 2)/3

→ x = (4/3)

and,

→ y = (dm + bn)/(m + n)

→ y = (2*2 + 5*1)/(2 + 1)

→ y = (4 + 5) / 3

→ y = 9/3

→ y = 3.

Hence, the co - ordinates of R is (4/3, 3) .

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Answer 2

Given :- P( -2,5) Q(3,2) are two points. find the co-ordinates of the point R on pq such that PR = 2QR ?

Solution :-

given that,

→ PR = 2 * QR

So,

→ PR / QR = 2 / 1 .

→ PR : QR = 2 : 1.

Now, we know that, section formula says that, if R(x,y) divides P(a, b) and Q(c, d) in ratio m : n , than :-

P(x , y) = (cm + an)/(m + n) , (dm + bn)/(m + n) .

from question we have :-

P(a, b) = (-2, 5)

Q(c, d) = (3 , 2)

m : n = 2 : 1

Putting all values we get :-

→ x = (cm + an)/(m + n)

→ x = (3 * 2 + (-2)*1) / (2 + 1)

→ x = (6 - 2)/3

→ x = (4/3)

and,

→ y = (dm + bn)/(m + n)

→ y = (2*2 + 5*1)/(2 + 1)

→ y = (4 + 5) / 3

→ y = 9/3

→ y = 3.

Hence, the co - ordinates of R is (4/3, 3) .

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prove that the mid point of the line joining points (-5,12) and (-1,12) is a point of trisection of the line joining the...

https://brainly.in/question/15118408

in what ratio is tge line joining the points (9, 2) and (-3, - 2 ) divided by the y axis? also find the coordinate of th...

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find the equation of the straight line which passes through the point 4,3 and parallel to line 3x +4y=7

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