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Question

The points on X-axis at a distance of 10 units from (11, –8) are __________.


A
(5, 0) and (16, 0)
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B
(6, 0) and (17, 0)
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C
(5, 0) and (17, 0)
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D
(5, 2) and (17, 0)
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Solution

The correct option is C (5, 0) and (17, 0)

We know that y-coordinate of a point on X-axis is always 0.

Therefore, the required points can be expressed in the form (x, 0), where x is the x-coordinate.

Distance between two points (x1,y1) and (x2,y2) is (x2x1)2+(y2y1)2.

Distance between (11, -8) and (x, 0) = 10 units (given)

(x11)2+82=102
x222x+121+64=100
x222x+85=0

On factorising the above equation, we get
x217x5x+85=0
(x17)(x5)=0
x=17 or 5

Hence, the required points are (17, 0) and (5, 0).


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