Question

Find the value of a, if the distance between the two points: (4,-5),(-2,a) is root85 units.​

Answer 1

Answer:

Given,

Points on the line :- ( 4 , -5 ) , (-2 , a)

Let,

A = ( 4 , -5 )

B = ( -2 , a )

Distance between two points i.e Distance Between A and B is $\sf\sqrt{85}$ units.

To Find :-

Value of 'a'.

Formula Required :-

$\sf\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Solution :-

Let ,

• x _1 = 4

• y_1 = -5

• x_2 = -2

• y_2 = a

According to question :-

$\sqrt{85} = \sqrt{( - 2 - 4) ^{2} + (a - ( - 5)) ^{2} }$

As there is square root on both side cancelling it on both side. So,

85 = ( -2 - 4)² + (a - (-5))²

85 = (-6)² + (a + 5)²

85 = 36 + a² + 2(a)(5) + (5)²

{$\sf\therefore$ (x + y)² = x² + 2xy + y²}

85 = 36 + a² + 10a + 25

85 = 61 + a² + 10a

a² + 10a = 85 - 61

a² + 10a = 24

a² + 10a - 24 = 0

a² +12a - 2a - 24 = 0

a (a + 12) -2(a + 12) = 0

(a - 2) (a + 12 ) = 0

i.e

(a - 2) = 0 (or) (a +12) = 0

a = 2 (or) a = -12

$\sf\therefore$ value of a = 2 (or) -12

Answer 2

Given that,

A= (4,-5)

B =(-2,a)

Distance between two points = √85 units

To Find:

value of (a)

Formula required : √(x1-x2)²-(y2-y1)²

Solution:

Let

x1= 4

x2= -2

y1= -5

y2 = a

A. T. Q

√85=√(x1-x2)²+(y2-y1)²

Cancel the square root on both sides

85=(x1-x2)²+(y2-y1)²

85= (-4-2)²+(a-(-5))²

85=(-6)²+( a+5 )²

85=(-6)²+(a+5)²

85=36+a²+2a×5+5²

by using (a+b)²=a²+2ab+b² formula

85=a²+10a+25

85=61+a²+10a

85-61=a²+10a

24=a²+10a

a²+10a-24=0

a²+12a-2a-24=0

a(a+12) -2(a+12) =0

(a-2) (a+12) =0

a=2 a=-12

value of a= 2or-12