Question

If the distance between the points (2,-2) and (-1, x) is 5, one of the values of x is :
(a) - 2
(b) 2
(c)-1
(d) 1
​

Answer 1

Step-by-step explanation:

correct answer is (b) 2

Answer 2

$\bigstar \underline{\underline{\mathfrak{Given:-}}}$

• Two points (2,2)&(-1,x).
• Distance btw them is 5.

$\bigstar \underline{\underline{\mathfrak{To\ find:-}}}$

• One of values of x.

$\bigstar \underline{\underline{\mathfrak{Solution:-}}}$

We know:

❥ Distance = (x2-x1)²-(y2-y1)²

Where (x1,x2)& (y1,y2) are two points of a line segment.

Now,

Substituiting the given values in the formula,

$:\implies \sf Distance=(x_2-x_1)^2+(y_2-y_1)^2\\\\:\implies 5^2=(-1-2)^2+(x+2)^2\\\\:\implies 25 =9^2+x^2+2+4x\\\\:\implies x^2 + 4x-12=0\\\\:\implies x^2+6x-2x-12=0\\\\:\implies x(x+6)-2(x+6)=0 \\\\:\implies (x-2)(x+6)=0=0\\\\:\implies x-2=0\ \ \ (or)\ \ \ x+6=0\\\\:\implies \boxed{\bold{x=2}} \ \ \ (or)\ \ \ \boxed{\bold{x=-6}}$

Hence, the two values of 'x' are 2,-6.

Acc to the options ,Option(B) is correct.

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HOPE IT HELPS !