Question

the distance between the points (1,3) and (x, 7) is 5 find x.......please give answer............​

Answer 1

Step-by-step explanation:

Let the points be A and B.

A=(1,3), B=(x,7)

x1=1, x2=x, y1=3, y2=7

Distance between the point A and B=5

$\sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } = 5$

$\sqrt{ { {(x - 1)}^{2} + {(7 - 3)}^{2} }} = 5$

$\sqrt{ {x}^{2} - 2x + 1 + 16 } = 5$

$\sqrt{ {x}^{2} - 2x + 17} = 5$

$squaring \: on \: both \: the \: sides$

${( \sqrt{ {x}^{2} - 2x + 17 }) }^{2} = {(5)}^{2}$

${x}^{2} - 2x + 17 = 25$

x²-2x+17-25=0

x²-2x-8=0

x²-4x+2x-8=0

(x²-4x)+(2x-8)=0

x(x-4)+2(x-4)=0

(x-4)(x+2)=0

(x-4=0)(x+2=0)

x=4 and x=(-2)

Therefore, x=4.