Question

distance between two points (X,7) and (1,15) is 10 units, find value of X

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Answer 1

Question:

The distance between two points (x, 7) and (1,15) is 10 units.Find the value of x .

Solution:

To find: Find the value of x.

Step-by-step explanation:

• Here,the distance between two points (x, 7) and (1, 15) is 10 units,so we should find the value of x.

❍Let us consider that, $\rm{x_1 = x,x_2 =1}$ and $\rm{y_1 = 7,y_2 =15}$

As we know that,

$\sf{Distance \: between \: two \: points \: AB = \sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}}$

Applying the values on given formula,

$\longrightarrow\sf{10 = \sqrt{ {(1 - x)}^{2} + {(15 -7 )}^{2} } } \\\longrightarrow\sf{10 = \sqrt{{(1 - x)}^{2} + {(8)}^{2}}} \\ \longrightarrow\sf{ 10 = \sqrt{{(1 - x)}^{2} + 64}} \\ \longrightarrow \sf{ {10}^{2} = {(1 - x)}^{2} + 64}\\\longrightarrow\sf{100 = {(1 - x)}^{2} + 64 } \\ \longrightarrow \sf{100 - 64 = {(1 - x)}^{2}} \\ \longrightarrow \sf{36 = {(1 - x)}^{2}} \\ \longrightarrow \sf{ \sqrt{36} = (1 - x) } \\ \longrightarrow \sf{ \pm \: 6 = (1 - x)} \\ \longrightarrow \sf{x = \pm \: 6 - 1} \\ \longrightarrow \sf{x = - 5(or)7}$

• Therefore,The value of x is -5 (or) 7.

________________________

Answer 2

Answer :

• x = -5 or 7

Solution :

Given :

• Distance between two points (X,7) and (1,15) is 10 units.

To Find :

• value of x.

We can find the value of x using Distance Formula. As it is given distance between two points is 10 Units and two points are (x ,7) and (1,15). So we will substitute the values in distance formula to get value of x.

$\red\bigstar\:\boxed{\sf AB = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}$

Here,

• $\sf (x_1,y_1) \: are \: (x , 7).$
• $\sf (x_2,y_2) \: are \: (1 , 15).$

$\LARGE \color{blue}\mathfrak{Substituting\:the\:values}$

$\implies\sf 10 = \sqrt{(1-x)^2+(15-7)^2}$

$\implies\sf 10 = \sqrt{(1-x)^2+(8)^2}$

• Squaring both the sides

$\implies\sf 10^2 = (1-x)^2+(8)^2$

$\implies\sf 100 = (1-x)^2+64$

$\implies\sf 36 = (1-x)^2$

• Square root both the sides

$\implies\sf \sqrt{36} = \sqrt{(1-x)^2}$

$\implies\sf ±6 = 1-x$

$\implies \sf 1-x = ±6$

$\implies \sf (1-x) = 6 \:\: or \:\: (1-x) = -6$

$\implies \sf 1-x = 6 \:\: or \:\: 1-x = -6$

$\implies \sf -x = 6-1 \:\: or\; \: -x = -6-1$

$\implies \sf -x = 5 \:\: or \:\: -x = -7 \\ \\ \implies \sf \underline{\boxed{\pink{\sf x = -5 \: \: or\: \: 7 }}}$

Hence,

value of x is 7 or -5.

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