Question

find the value of x so that the distance between the points (-3, 4) and (x, --4) is 10​

Answer 1

Answer:

don't know but for points

Answer 2

Given:

1st point = (-3, 4)

2nd point= (x, -4)

Distance between the two points= 10

To find:

The value of x.

Solution:

We know that formula for distance between two points is:

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

Where the two points are (x2, y2) and (x1, y1)

Comparing the values given in the question:

(x2, y2) = (x, -4)

(x1, y1) = (-3, 4)

$d = \sqrt{ {(x - ( - 3))}^{2} + {( - 4 - 4)}^{2} }$

$10 = \sqrt{ {(x + 3)}^{2} + {( - 8)}^{2} }$

On squaring both the sides we get:

$100 = {(x + 3)}^{2} + 64$

Shifting 64 on the other side:

$100 - 64 = {(x + 3)}^{2}$

On expanding the equations we get:

$16 = {x}^{2} + 9 + 6x$

${x}^{2} + 6x - 7 = 0$

By Factorization method:

${x}^{2} + 7x - x - 7 = 0$

$x(x + 7) - 1(x + 7) = 0$

$(x + 7)(x - 1) = 0$

$x = - 7 \: and \: 1$

Therefore the value of x is -7 and 1.