A is a point on the x-axis and B is the distance between the points A and B is 50 units. find the coordinates of point A
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The given question is incomplete. Another similar question is
A is a point on the x axis and B is -2,9 distance between the points A and B is 15 units .
The coordinates of A is (-14,0) or (10,0)
Le the x-coordinate of the point A be x.
So, the point A lying on the x-axis is (x,0)
B is (-2,9)
Distance between two points (x1,y1) and (x2,y2) is given as:
D = √[(x2-x1)²+(y2-y1)²]
Here,
x2 = -2
x1 = x
y2 = 9
y1 = 0
So, D = √[(-2-x)²+(9-0)²]
This is equal to 15. So,
15 = √[(2+x)²+9²]
⇒ √(x²+4x+4+81) = 15
⇒ √(x²+4x+85) = 15
Squaring both sides, we get,
x²+4x+85 = 225
⇒ x²+8x-140 = 0
⇒ x²+ 14x - 10x - 140 = 0
⇒ x(x+14) -10(x+14) = 0
⇒ (x+14)(x-10) = 0
x = 10, -14.
So, A is (10,0) or (-14,0)
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