Question

if the distance between the points (3,a) and (6,1) is 5,find the value of a?​

Answer 1

Answer:

a=5 or -3

Step-by-step explanation:

$\sqrt{-3^{2}+(a-1)^2 }$ =5

SOBS

9+(a-1)^2=25

(a-1)^2=16

a-1=+4 or -4

a=5 or -3

Answer 2

The value of a is 5.

Step-by-step explanation:

Given : If the distance between the points (3,a) and (6,1) is 5.

To find : The value of a?​

Solution :

The distance formula of two points is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Here, $(x_1,y_1)=(3,a)$ ,  $(x_2,y_2)=(6,1)$ and d=5

$5=\sqrt{(6-3)^2+(1-a)^2}$

Squaring both side,

$25=(3)^2+(1-a)^2$

$25=9+1+a^2-2a$

$a^2-2a-15=0$

$a^2-5a+3a-15=0$

$a(a-5)+3(a-5)=0$

$(a-5)(a+3)=0$

$a=5,-3$

Reject a=-3.

The value of a is 5.

#Learn more

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