Question

3. find the values of y for the which the distance
between the the point P (2, 3) andQ(10,y)
(hint d=10 units)
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Answer 1

the formula to calculate the distance between two points (a,b) and (c,d) is given by
dist d = √(a-c)² + (b-d)²

applying it for this ques we have d=10 units
10 = √(2 - 10)² + (-3-y)²
squaring both sides
100 = (-8)² + (9 + y² + 6y)
100 = 64 +9 + y² + 6y
y² + 6y - 27 = 0
y² + 9y - 3y - 27 = 0
y(y + 9) -3(y + 9) = 0
(y-3)(y+9) = 0
y=3 or y=-9

both values of y are possible unless no other condition is specified in the question.


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Answer 2

AB² = (x2-x1)² + (y2-y1)²

10² = (10-2)² + (y-3)²

100 = 8² + (y² - 6y + 9)

100 = 64 + y² -6y + 9

100 = 73 + y² -6y

y² - 6y +73 - 100 = 0

y² - 6y -27 = 0

y² -9y + 3y - 27 = 0

y(y-9) + 3(y-9) = 0

(y+3)(y-9) = 0

y = -3 or y = 9

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