Question

radius,
18. The distance between (3,x) and (-7,2) is 10. Find the value of 'x'​

Answer 1

Answer:

x = 2

Step-by-step explanation:

Distance formula is

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

d = 10, (x1, y1) = (3, x), (x2, y2) = (-7, 2)

$10 = \sqrt{ {( - 7 - 3)}^{2} + {(2 - x)}^{2} }$

Squaring on both sides,

$100 = {( - 10)}^{2} + {(2 - x)}^{2}$

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

${(2 - x)}^{2} = 100 - 100$

${(2 - x)}^{2} = 0$

$(x - 2)(x - 2) = 0$

x = 2, 2

x = 2 units

(if you find this answer helpful mark me brainliest)

Answer 2

✅ Verified Answer

Given :

• x1 = 3 , x2 = -7
• y1 = x , y2 = 2
• Distance between them is 10 units

to find : value of x

$\sf {(distance)}^{2} \: \: = {( { }^{ \large x} {2}^{ \: } - { }^{ \large x} {1}^{ \: } )}^{2} + {( { }^{ \large y} {2}^{ \: } - { }^{ \large y} {1}^{ \: } )}^{2}$

then ,

$\sf {(10)}^{2} = {( - 7 - 3)}^{2} + {(2 - x)}^{2}$

$\sf 100 = {( - 10)}^{2} + {(2 - x)}^{2}$

$\sf 100 = 100 + 4 + {x}^{2} \: \: \implies \: \: 100 = 104 + {x}^{2}$

$\sf {x}^{2} = 100 - 104 = - 4 \: \: \implies \: \: {x}^{2} = - 4$

$\sf x = \sqrt{ - 4} = ± 2$

Mark as Brainliest answer please my friend