Question

It the distance between two points (x, 7) and (1, 15) is 10 . find the volved of x​

Answer 1

Answer:-

There are two values of x are possible,x = -5and x = 7.

Explanation:-

Given:-

• Two points (x, 7) and (1, 15).

• Distance between the points is 10 units.

To Find:-

• The Value of x.

ID Used:-

$\\ \large \orange{ \leadsto \boxed{ \red{ \bf (a - b) {}^{2} = {a}^{2} - 2ab + {b}^{2} .}}}$

Formula Used:-

$\\ \large \red{ \leadsto \boxed{ \pink{ \bf d = \sqrt{(x_2 - x_1) {}^{2} + (y_2 - y_1) {}^{2} }.}}}$

Where,

• d = Distance between the given two points.

• $\tt x_2\:\: and\:\:x_1$ Are the x coordinates of given two points.

• $\tt y_2\:\: and\:\:y_1$ Are the y coordinates of given two points.

So Here,

• d = 10 units.

• $\tt y_2\:\: and\:\:y_1$ 15 amd 7 respectively.

• $\tt x_2$ = 1.

• $\tt x_1$ = x [To Find].

Now,

By putting the above values in the formula we get,

$\\ \bf \mapsto d = \sqrt{(x_2 - x_1) {}^{2} + (y_2 - y_1) {}^{2} }.$

$\\ \rm\mapsto 10= \sqrt{(1 - x) {}^{2} + (15 - 7) {}^{2} }.$

$\\ \rm\mapsto(10) {}^{2} = \bigg( \sqrt{(1 - x) {}^{2} + (15 - 7) {}^{2} } \bigg). \\ \rm(squaring \: \: both \: \:the \: \: sides)$

$\\ \rm\mapsto100 = (1 - x) {}^{2} + (8) {}^{2} .$

$\\ \rm\mapsto100 = 1 - 2x + {x}^{2} + 64. \\ \rm(by \: \: using \: \: id).$

$\\ \rm\mapsto100 = {x}^{2} - 2x + 65.$

$\\ \rm\mapsto x {}^{2} - 2x + 65 - 100 = 0.$

$\\ \rm\mapsto {x}^{2} - 2x - 35 = 0.$

$\\ \rm\mapsto {x}^{2} - (7 - 5)x - 35 = 0. \: \: \: \: \: \\ \rm(by \: \: splitting \: \: middle \: \: term).$

$\\ \rm\mapsto {x}^{2} - 7x + 5x - 35 = 0.$

$\\ \rm\mapsto x(x - 7) + 5(x - 7) = 0.$

$\\ \rm\mapsto(x - 7)(x + 5) = 0.$

$\\ \tt\mapsto \: \: \rm either \: (x - 7) = 0 \: \: \: \: or \: \: \: \: (x + 5) = 0.$

$\\ \tt\mapsto \: \: \rm either \: x = 0 + 7 \: \: \: \: or \: \: \: \: x = 0 - 5.$

$\\ \large \red{ \mapsto \boxed{ \blue{ \rm either \: \: x = 7 \: \: \: \: or \: \: \: \: x = - 5.}}}$

$\bf\therefore$ The Required Values Of x Are 7 and -5.