Question

If the distance between the points (x,-1) and (3, 2) is 5, then the value of x is
(a) -7 or -1
(b)-7 or 1
(c) 7 or 1
(d) 7 or -1​

Answer 1

Answer:

(d) 7 or -1

Step-by-step explanation:

Using Distance formula

$\sqrt{ {(x - 3)}^{2} + { (- 1 - 2)}^{2} } = 5 \\ squaring \: both \: sides \\ {(x - 3)}^{2} + { ( - 3)}^{2} = 25 \\ {(x - 3)}^{2} + 9 = 25 \\ {(x - 3)}^{2} = 25 - 9 = 16 \\ taking \: square \: root \: on \: both \: sides \\ |x - 3| = 4 \\ x - 3 = 4 \: or \: x - 3 = - 4 \\ x = 7 \: or \: x = - 1$

Answer 2

Answer:

Step-by-step explanation:

If the distance between the points (x,-1) and (3, 2) is 5

we know that √(x-3)²+(-1-2)²=5

square both side

(x-3)²+(-1-2)²=5²

Or,x²-6x+9+9=25

Or,x²-6x+18=25

Or,x²-6x-7=0

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

x=7,x=-1

(d) 7 or -1​ correct answer