Question

the value of a if the distance between the points A(-3, -14) and B(a, -5) is 9 units​

Answer 1

Given

We have given the distance between A(-3,-14) and B(a,-5) is 9 units

To Find

We have to find the value of 'a'

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

How to solve

step 1:We will use distance formula because distance is given and points are given.

Step 2: Now, Equate the both sides and hence we will find the value of a .

A(-3,-14) & B (a,-5) and distance is 9 units

Distance formula

Distance formulaD=√(x₂- x₁)²+(y₂- y₁)²

Distance between A and B

A (-3,-14) & B( a,-5)

x₁= -3;x₂ =a ; y₁= -14 & y₂ = -5

Distance between AB

=> 9= √{ (a-(-3)}²+(-5-(-14))²

=>9=√(a+3)²+(-5+14)²

=>9= √(a+3)²+9²-------(1)

Identity ➙(a+b)²=a²+b²+2ab

=>9=√ a²+3²+2(a)(3)+(9)²

=>9= √a²+9+6a+81

=>9= √ a²+6a +81

Squaring both sides

=> 81= a²+6a +81

=> a²+6a = 81-81

=>a²+6a = 0

=>a(a+6)=0

a= 0 or a = -6

Answer 2

Step-by-step explanation:

Given

We have given the distance between A(-3,-14) and B(a,-5) is 9 units

To Find

We have to find the value of 'a'

$\sf\huge \mathbb{\underline{\underline{{Solution}}}} </p><p>Solution</p><p> </p><p> </p><p>$

How to solve

step 1:We will use distance formula because distance is given and points are given.

Step 2: Now, Equate the both sides and hence we will find the value of a .

A(-3,-14) & B (a,-5) and distance is 9 units

Distance formula

Distance formulaD=√(x₂- x₁)²+(y₂- y₁)²

Distance between A and B

A (-3,-14) & B( a,-5)

x₁= -3;x₂ =a ; y₁= -14 & y₂ = -5

Distance between AB

=> 9= √{ (a-(-3)}²+(-5-(-14))²

=>9=√(a+3)²+(-5+14)²

=>9= √(a+3)²+9²-------(1)

Identity ➙(a+b)²=a²+b²+2ab

=>9=√ a²+3²+2(a)(3)+(9)²

=>9= √a²+9+6a+81

=>9= √ a²+6a +81

Squaring both sides

=> 81= a²+6a +81

=> a²+6a = 81-81

=>a²+6a = 0

=>a(a+6)=0

a= 0 or a = -6