If point B(0, 1) is equidistant from points A(5, -3) and C(x, 6), then find the values of x.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → ±4
B is equidistant from A and C, so \(BA=BC\); it is easier to equate their squares, using the distance formula \(d^2=(x_2-x_1)^2+(y_2-y_1)^2\).
From B(0, 1) to A(5, −3): \(BA^2=(5-0)^2+(-3-1)^2=25+16=41\)
From B(0, 1) to C(\(x\), 6): \(BC^2=(x-0)^2+(6-1)^2=x^2+25\)
The two distances are equal: \(x^2+25=41\), so \(x^2=16\)
Both square roots fit, so \(x=\pm4\): C can be (4, 6) or (−4, 6)