Question

- If the distance between the point (3.a) and (3.1) is 2 ,then the value of a is​

Answer 1

Given

The distance between the point (3,a) and (3,1)

is 2

To Find

Value of a

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Step by step explanation

To find the distance between any two points we use distance formula to find out the distance between any two given points.

Now,we will apply distance formula and put points in the formula and put the distance value which is 2 in the front of the formula.

Now,let the point be A(3,a) B(3,1)

Distance formula=

$\sf D= \sqrt{ {(x_{2} - x_{1})}^{2} + {(y_{2 }- y_{1})}^{2} }$

$\sf \sqrt{ {(3 - 3)}^{2} + {(1 - a)}^{2} } =2$

$\sf \sqrt{ {(0)}^{2} + {(1)}^{2} + {a}^{2} - 2a } = 2$

$\sf \sqrt{1 + {a}^{2} - 2a } = 2$

Now, squaring both sides

$\sf \longmapsto {a}^{2} - 2a + 1 = 4$

$\sf \longmapsto {a}^{2} - 2a + 1 - 4$

$\sf \longmapsto {a}^{2} - 2a - 3 = 0$

Now,it is in the form of a quadratic equation so we factorise it .

$\sf \longmapsto {a}^{2} - 3a + a - 3 = 0$

$\sf \longmapsto a(a - 3) + 1(a - 3) = 0$

$\sf \longmapsto(a + 1)(a - 3) = 0$

$\sf a + 1 = 0$

$\sf { \bold{a = - 1}}$

$\sf a - 3 = 0$

$\sf \longmapsto{ \bold{a = 3}}$

$\therefore$$\bold{a\: is \:either }$$\bold{\red{-1 \:or \:3}}$