Question
What point on the $x-$axis is equidistant from the points $(7, 6)$ and $(-3, 4)$?
✓
Answer
Let the co$-$ordinates of the required point on $x-$axis be $P (x, 0).$
The given points are $A (7, 6)$ and $B (-3, 4).$
Given,$\text{PA} =\text{PB}$
$PA^2 = PB^2$
$(x - 7)^2 + (0 - 6)^2 = (x + 3)^2 + (0 - 4)^2$
$x^2+ 49 - 14x + 36 = x^2 + 9 + 6x + 16$
$60 = 20x$
$x = 3$
Thus, the required point is $(3, 0).$
The given points are $A (7, 6)$ and $B (-3, 4).$
Given,$\text{PA} =\text{PB}$
$PA^2 = PB^2$
$(x - 7)^2 + (0 - 6)^2 = (x + 3)^2 + (0 - 4)^2$
$x^2+ 49 - 14x + 36 = x^2 + 9 + 6x + 16$
$60 = 20x$
$x = 3$
Thus, the required point is $(3, 0).$
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