Question

find the point the point on x axis which is equidistant from the following pair of points (5,-2) and( -3,2)

Answer 1

Answer:

$(1,0)$

Step-by-step explanation 1:

Formula Of Distance Between Two Points

Let the point on the x-axis be $(x,0)$.

I use the distance formula and find the value.

Pythagorean Theorem - Distance Between Two Points

A point $(x_1,y_1)$ and another point $(x_2,y_2)$ forms a right triangle,

which has a longest side $d$.

We use the Pythagorean theorem and find that :

• $d^2=(x_2-x_1)^2+(y_2-y_1)^2$

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Step-by-step explanation 2:

Let the equal distance $d$.

Then, $d^2=(x-5)^2+2^2=(x+3)^2+2^2$.

We use $(x-5)^2+2^2=(x+3)^2+2^2$ to find x.

$x^2-10x+25+4=x^2+6x+9+4$

$-10x+29=6x+13$

$-16x=-16$

∴ $x=1$

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Answer 2

Step-by-step explanation:

let the point on x axis be A(x, 0)

so, p(5,-2) and Q(-3,2)

so, PA=QA

√(5-x)^2+(-2-0)^2=√(-3-x)^2+(2-0)^2

squaring both sides

(5-x)^2+(-2)^2=(-3-x)^2+(2)^2

25+x^2-10x+4=9+x^2+6x+4

x^2-10x+29=x^2+6x+13

x^2-10x+29-x^2-6x-13=0

-16x+16=0

-16x=-16

x=-16÷-16=1

so the point on x axis is (1,0)