(b) multiple of 3
Given :
The distance between two points A and B, on a graph is given as \(\sqrt {10^2+7^2}\)
The coordinates of A are (−4,3)
Given that the point B lies in the first quadrant
To find :
The possible x-coordinates of point B are
(a) multiple of 2
(b) multiple of 3
(c) multiple of 5
(d) multiple of 6
Form the equation to find the value of x-coordinates of point B
Let coordinates of the point B is (x, y)
The distance between two points A and B, on a graph is given as \(\sqrt {10^2+7^2}\)
The coordinates of A are (−4,3)
By the given condition
\(\sqrt {(x+4)^2+ (y-3)^2}= \sqrt {10^2 + 7^2}\)
Find all possible x-coordinates of point B
Given that the point B lies in the first quadrant
Now two cases arise
Case : 1
From Equation 1 we get
(x + 4) = 10 and (y - 3) = 7
Consequently, x = 6 , y = 10
In that case the coordinates of B is (6,10)
In that case x-coordinates of point B is 6
Case : 2
From Equation 1 we get
(x + 4) = 7 and (y - 3) = 10
Consequently, x = 3 , y = 13
In that case the coordinates of B is (3,13)
In that case x-coordinates of point B is 3
The possible x-coordinates of point B are 3 and 6
Hence the correct option is (b) multiple of 3
