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Question
The abscissa of a point A is equal to its ordinate, and its distance from the point B(1, 3) is 10 units, What are the coordinates of A?
The abscissa of a point A is equal to its ordinate, and its distance from the point B(1, 3) is 10 units, What are the coordinates of A?
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Solution
The correct option is A (-5,-5), (9,9)
Let point A=(a,a)
Distance of AB = 10
Then, √(x2−x1)2+(y2−y1)2=10
i.e, √(a−1)2+(a−3)2=10(a−1)2+(a−3)2 = 100
a2−2a+1+a2−6a+9 = 1002a2−8a+10=100a2−4a−45=0(a−9)(a+5)=0a=9 or −5
i.e, A= (9,9) or (-5,-5)
Let point A=(a,a)
Distance of AB = 10
Then, √(x2−x1)2+(y2−y1)2=10
i.e, √(a−1)2+(a−3)2=10(a−1)2+(a−3)2 = 100
a2−2a+1+a2−6a+9 = 1002a2−8a+10=100a2−4a−45=0(a−9)(a+5)=0a=9 or −5
i.e, A= (9,9) or (-5,-5)
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