Question

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

Answer 1

Answer: IHOPE IT IS BETTER AND HELPFUL ANSWER FOR YOU

PLEASE BRAINLIEST MY ANSWER

a = -14±√77

Step-by-step explanation:

We know that the formula for the distance between two points

d = √[(x$_{2}$ - x$_{1}$)²+(y$_{2}$ - y$_{1}$)²]

A(-5,a) ≡ (x$_{1}$,y$_{1}$)       ;       B(-3,-14) ≡ (x$_{2}$,y$_{2}$ )

∴d = √{ [(-3)-(-5)]² + [(-14)-(a)]² }

 9 = √{ (2)² + [(-14)-a]² }

 9 = √{ 4 + [(-14)-a]² }

square on both side

 9² = { 4 + [(-14)²+2*(-14)*(-a)+(-a)²] }

81  = { 4 + 196 + 28a + a² }

81  =  200 + 28a + a²

a² + 28a + 200 - 81  = 0

a² + 28a + 119 = 0

Now we know that the formula for finding x from equation,

px²+qx+r = 0 is

x = [-q±√(q²-4pr)]/2p

compare both equation we get

p=1, q=28, r=119

a = {-28±√[(28)²-4*1*119]}/2*1

a = {-28±√[784-476]}/2

a = {-28±√(308)}/2

a = {-28±√(4*77)}/2

a = {-28±2√77}/2 = 2[-14±√77] / 2 = -14±√77

∵  a  = -14±√77