Question

find the value of a if the points (3, 5) and (7, 1) equidistant from the points (a,0)

Answer 1

HEY BUDDY..!!!!

HERE'S THE ANSWER...


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▶️ We will be using following formula known as distance formula.

✔️ If we had give 2 points ( x1 , y1 ) and ( x2 , y2 ). Then distance between these 2 points will be given by

⏺️ d = √ [ ( x2 - x1 )^2 + ( y2 - y1 )^2 ]

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▶️ Given AO = BO, ( 3 , 5 ) , ( a , 0 )

=> x1 = 3 , x2 = a , y1 = 5 , y2 = 0


⏺️ Now we'll find AO

=> d = √ [ ( x2 - x1 )^2 + ( y2 - y1 )^2 ]

=> AO = √ [ ( x2 - x1 )^2 + ( y2 - y1 )^2 ]

=> AO = √ [ ( a - 3 )^2 + ( 0 - 5 )^2 ]

=> AO = √ [ ( a - 3 )^2 + ( 5 )^2 ]

=> AO = √ [ ( a )^2 + 9 - 6 a + 25 ]

=> AO = √ [ ( a )^2 + - 6 a + 34 ]

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▶️ Now we will find BO , ( 7 , 1 ) , ( a , 0 )

=> x1 = 7 , x2 = a , y2 = 0 , y1 = 1

=> d = √ [ ( x2 - x1 )^2 + ( y2 - y1 )^2 ]

=> BO = √ [ ( a - 7 )^2 + ( 0 - 1 )^2 ]

=> BO = √ [ ( a - 7 )^2 + ( 1 )^2 ]

=> BO = √ [ ( a )^2 + 49 - 14 a+ 1 ]

=> BO = √ [ ( a )^2 - 14 a + 50 ]


⏺️ We know AO = BO

=> √ [ ( a )^2 + - 6 a + 34 ] = = √ [ ( a )^2 - 14 a + 50 ]

⏺️ Squaring both sides

=> ( a )^2 + - 6 a + 34 = ( a )^2 - 14 a + 50

=> - 8 a = - 16

=> [ a = 2 ]✔️✔️

▶️ So point On is ( 2 , 0 )




HOPE HELPED..


JAI HIND. !!


:-)

Answer 2

a = 2.......... ........