Class 10 Math All topics Coordinate Geometry

Find the coordinates of the point equidistant from three given points $A(5,3),B(5,−5)$ and $C(1,−5)$.

Solution:

Let the coordintaes of the point be $O(x,y)$, then

$OA=OB=OC$

or $OA_{2}=OB_{2}=OC_{2}$

$OA_{2}=(5−x)_{2}+(3−y)_{2}$

$OB_{2}=(5−x)_{2}+(−5−y)_{2}$

$OC_{2}=(1−x)_{2}+(−5−y)_{2}$

$(5−x)_{2}+(3−y)_{2}=(5−x)_{2}+(−5−y)_{2}$

$9−6y+y_{2}=25+10y+y_{2}$

$9−25=10y+6y$

$⇒16y=−16$

$y=16−16 =−1$

and $(5−x)_{2}+(−5−y)_{2}$

$=(1−x)_{2}+(−5−y)_{2}$

$25−10x+x_{2}=1−2x+x_{2}$

$−10x+2x=1−25$

$−8x=−24$

or $x=3$

So, coordinates of the point is $(3,1)$.

Similar topics

introduction to trigonometry

functions

some applications of trigonometry

quadratic equations

surface areas and volumes

introduction to trigonometry

functions

some applications of trigonometry

quadratic equations

surface areas and volumes

Related Questions

Related Questions