Q. 354.0( 25 Votes )

Find the values o

Answer :

Given:  the distance between the points P (2, -3) and Q (10, y) is 10 units.
To find: The value of y.
Solution:
Coordinates are P (2, -3) and Q (10, y)


We use distance formula to find the distance between two points.


Since PQ = 10 units
S0,

= 10


On squaring both sides, we get


= 100


⇒ 82 + (y+3)2 = 100

⇒ = 100
⇒ 73 + y2 + 6y = 100
⇒ 73 + y2 + 6y -100 = 0
⇒ = 0
In factorization, we write the middle term of the quadratic equation either as a sum of two numbers or difference of two numbers such that the equation can be factorized.

⇒ y2 + 9y - 3y - 27 = 0

⇒y(y + 9) - 3(y + 9) = 0

⇒(y - 3)(y + 9) = 0

⇒y = 3, -9

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