MCQ
Which point on $x-$axis is equidistant from the points $A(7, 6)$ and $B(-3, 4)$?
- A$(0, 4)$
- B$(-4, 0)$
- ✓$(3, 0)$
- D$(0, 3)$
✓
Answer
Correct option: C.
$(3, 0)$
Let the coordinates of the point be $P(x, 0)$
Since the point lies on the $x-$axis. $P$ is equidistant from $A(7, 6)$ and $B(-3, 4)$
Using the distance from, we get
$AP^2 = BP^2$
$\Rightarrow (7 - x)^2 + (6 - 0)^2 = (-3 - x)^2 + (4 - 0)^2$
$\Rightarrow 49 - 14x + x^2 + 36 = 9 + 6x + x^2 + 16$
$\Rightarrow 85 - 14x = 6x + 25$
$\Rightarrow 20x = 60$
$\Rightarrow x = 3$
Thus, the point $(3, 0)$.
Since the point lies on the $x-$axis. $P$ is equidistant from $A(7, 6)$ and $B(-3, 4)$
Using the distance from, we get
$AP^2 = BP^2$
$\Rightarrow (7 - x)^2 + (6 - 0)^2 = (-3 - x)^2 + (4 - 0)^2$
$\Rightarrow 49 - 14x + x^2 + 36 = 9 + 6x + x^2 + 16$
$\Rightarrow 85 - 14x = 6x + 25$
$\Rightarrow 20x = 60$
$\Rightarrow x = 3$
Thus, the point $(3, 0)$.
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