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

Explanation

According to the question,
Distance between A(-3,-14) and B(a,-5), AB=9
[`:'` distance between two points `(x_(1),y_(1))and(x_(2),y_(2))`,d`=sqrt((x_(2)-x_(1))+(y_(2)-y_(1))^(2))]`
`rArr sqrt((a+3)^(2)+(-5+14)^(2))=9`
`rArr sqrt((a+3)^(2)+(9)^(2))=9`
On squaring both the sides , we get
`(a+3)^(2)+81=81`
`rArr(a+3)^(2)` `=0rArra=-3`
Hence , the required value of a is -3.