Write a formula for the distance from A = (−1, 5) to P = (x, y), and another formula for the distance from P = (x, y) to B = (5, 2). Then write an equation that says that P is equidistant from A and B. Simplify your equation to linear form.
Write a formula for the distance from A = (−1, 5) to P = (x, y), and another formula for the distance from P = (x, y) to B = (5, 2). Then write an equation that says that P is equidistant from A and B. Simplify your equation to linear form.
1. Based on the Pythagorean theorem the distance between the points $\displaystyle P(x_P, y_P)$ and $\displaystyle Q(x_Q, y_Q)$ is calculated by:
$\displaystyle d(P,Q)=\sqrt{(x_P - x_Q)^2+(y_P-y_Q)^2}$
2. You'll get the equation
$\displaystyle d(A,P) = d(B, P)$
i) Square both sides of the equation.
ii) Expand the brackets.
iii) Collect like terms - and you're done.