Question

find the co ordinates of the point Q on the x axis which lies on perpendicular bisextor of the line segment joining the points A(-5,-2) and B (4,-2) . name the triangle formed by Q, A, and B . plz don't spam .
tommorow is my paper​

Answer 1

Answer:

Explanation:

The point Q lies on the x-axis.

So, its co-ordinate will be of the form (x,0)

Let's take the points as Q(x,y)=(x,0) which is equidistant from A(5,2) and B(4,2)

To find the distance, we use distance formula

d=  

(x  

2

​  

−x  

1

​  

)  

2

+(y  

2

​  

−y  

1

​  

)  

2

 

​  

 

⟹AQ=  

(x−x  

1

​  

)  

2

+(y−y  

1

​  

)  

2

 

​  

=  

(x−5)  

2

+(0−2)  

2

 

​  

 

and BQ=  

(x−x  

2

​  

)  

2

+(y−y  

2

​  

)  

2

 

​  

=  

(x−4)  

2

+(0−2)  

2

 

​  

 

But AQ=BQ

∴  

(x−5)  

2

+(0−2)  

2

 

​  

=  

(x−4)  

2

+(0−2)  

2

 

​  

 

⟹x=  

2

9

​  

=4.5

∴ The co-ordinates of Q is (4.5,0)

∵AQ=BQ and Q lies on the perpendicular bisector of AB

Therefore, the ΔABQ is an isosceles triangle.