The point on the x-axis which is equidistant from (3, 4) and (4, 5) is
Answers
Answer:
Distance
between two points (x
1
,y
1
) and (x
2
,y
2
) can be calculated using the formula
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
Let the point on the x-axis be (x,0)
Distance between (x,0) and (5,4)=
(5−x)
2
+(4−0)
2
=
5
2
+x
2
−10x+16
=
x
2
−10x+41
Distance between (x,0) and (−2,3)=
(−2−x)
2
+(3−0)
2
=
2
2
+x
2
+4x+9
=
x
2
+4x+13
As the point (x,0) is equidistant from the two points, both the distances calculated are equal.
x
2
−10x+41
=
x
2
+4x+13
Taking square on both the side
⇒x
2
−10x+41=x
2
+4x+13
41−13=10x+4x
28=14x
x=2
Thus, the point is (2,0)
ANSWER
Distance
between two points (x1,y1) and (x2,y2) can be calculated using the formula (x2−x1)2+(y2−y1)2
Let the point on the x-axis be (x,0)
Distance between (x,0) and (5,4)=(5−x)2+(4−0)2=52+x2−10x+16=x2−10x+41
Distance between (x,0) and (−2,3)=(−2