Question

If the distance between the points (-1,4) and
(4,9) is 13 units then sind the value of y.​

Answer 1

Answer:

Let A and B be the two points such that A(3,x) and (−2,−6) respectively.

AB=13 units(Given)

As we know that distance between the two points (x  

1

​  

,y  

1

​  

) and (x  

2

​  

,y  

2

​  

) is-

d=  

(x  

2

​  

−x  

1

​  

)  

2

+(y  

2

​  

−y  

1

​  

)  

2

 

​  

 

Therefore,

AB=  

(−2−3)  

2

+(−6−x)  

2

 

​  

 

⇒AB=  

25+(36+x  

2

+12x)

​  

 

But given that AB=13 units

∴  

25+(36+x  

2

+12x)

​  

=13

Squaring both sides, we have

(  

25+(36+x  

2

+12x)

​  

)  

2

=(13)  

2

 

25+36+x  

2

+12x=139

x  

2

+12x+61−139=0

x  

2

+12x−78=0

Now by quadratic formula, we have

x=  

2×1

−12±  

(12)  

2

−4(−78)(1)

​  

 

​  

 

⇒x=  

2

−12±  

144+312

​  

 

​  

 

⇒x=  

2

−12±  

456

​  

 

​  

 

⇒x=−6±  

114

​  

 

Hence the value of x is (−6+  

114

​  

) or (−6−  

114

​  

).

Step-by-step explanation:

$\sqrt{x} 114$