Question

A point p is at a distance of root 13 unit from the point (5, 4).find the coordinate of point p, if its ordinate is trice of its abscissa
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Answer 1

Answer:

Either (2, 6) or (7/5, 21/5)

Step-by-step explanation:

We know that, the co-ordinates of point P is. (a, 3a) as given, ordinate is thrice of its abscissa.

And, given, the point P is at a distance of root of 13 from the points (5,4)

√{(5 - a)2 + (4 - 3a)2 } = √13

Or, (5 - a)2 + (4 - 3a)2 = 13

Or, 25 + a2 - 10a) + (16 + 9a2 - 24a) = 13

Or, 25 + a2 - 10a + 16 + 9a2 - 24a = 13

Or, 41 + 10a2 - 34a = 13

Or, 10a2 - 34a + 41 - 13 = 0

Or, 10a2 - 34a + 28 = 0

Or, 2 (5a2 -17a + 14) = 0

Or, (5a2 -17a + 14) = 0

Or, 5a2 - 10a - 7a + 14 = 0

Or, 5a(a - 2) - 7(a - 2) = 0

Or, (a - 2) (5a - 7) = 0

Either, (a - 2) = 0 Or, (5a - 7) = 0

=> a =2 => a = 7/5

Here, a = 2 , 7/5

So, 3a = 6, 21/5

Hence, the required point is either (2, 6) or (7/5, 21/5)

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