Question

Find the value of a when the distance between the points (3,a)and(4,1) is root10​

Answer 1

Answer:

Step-by-step explanation:

Let the given points are A( 3 , a ) and B ( 4, 1 ).

Then,

X1 = 3 , X2 = 4 and Y1 = a , Y2 = 1

We have :

AB = √10 => AB² = (√10)²

=> AB² = 10

=> ( 4 - 3 )² + ( 1 - a )² = 10

=> (1)² + (1 - a )² = 10

=> ( 1 - a )² = 10 - 1

=> ( 1 - a )² = 9

=> ( 1 - a )² = (3)²

=> 1 - a = +- 3

=> 1 - a = 3 or 1 - a = -3

=> -a = 3 - 1 or -a = -3 - 1

=> -a = 2 or -a = -4

=> a = -2 or a = 4.

Answer 2

Given:-

• The distance between the points (3,a)and(4,1) is root10.

To find:-

• Find the value of a..?

Solutions:-

The distance d between two point (x1, y1) and (x2, y2) is given by the formula.

• d = √(x1 - x2)² + (y1 - y²)²

The distance between two points (3, a) and (4, 1) is given as √10

=> √10 = √(3 - 4)² + (a - 1)²

=> √10 = √( - 1)² + (a - 1)²

Now, Squaring the above equation on both sides of the equals sign.

=> 10 = (-1)² + (a - 1)²

=> 10 = 1 + (a² + 1 - 2a)

=> 10 = 1 + a² + 1 - 2a

=> 10 = 2 + a² - 2a

=> 10 - 2 = a² - 2a

=> 8 = a² - 2a

Thus, we arrive at a quadratic equation.

=> a² - 2a - 8 = 0

=> a² - 4a + 2a - 8 = 0

=> a(a - 4) + 2(a - 4) = 0

=> (a - 4) (a + 2) = 0

The roots of the quadratic equation are 4 and -2.

Hence, the value of a is 4 and -2.