Question

Determine the coordinates of the point p on the line y=-x+6 such that p is equidistant from the points a(10,-10) and o(0,0) (that is, so that pa=po). express your answer as an ordered pair (a,b).

Answer 1

Solution,

Let P =  ( x, -x + 6) = (x, 6 - x)

We want to solve this

( Distance from P to (0,0) )^2  = (Distance from P to (10, -10) )^2

x^2 + (6 - x)^2  =  [ ( x - 10)^2 + ( 6 - x + 10)^2

x^2 + x^2 - 12x + 36  =   x^2 - 20x + 100  + x^2 - 32x + 256     simplify

-12x + 36  =  -52x + 356

40x =  320

x = 8

And y = -(8) + 6  =  -2

So...P  =  ( 8, -2)

In mathematics, an equation is an equation that expresses two equations by joining them with an equal sign =. Equations in other languages ​​and the word their relatives can have slightly different meanings; for example, in French, an equation is defined as containing one or more variables, but in English, it is an equal sign.

A well-formed expression consisting of two combined equations is an equation, and a variable makes the equation true. The variable for which the equation must be solved is also called the unknown, and the value of the unknown that satisfies the equation is called the solution of the equation. There are two types of equations: identities and constraint equations. The ID applies to all values ​​of the variable. Constraint equations apply only to specific values ​​of variables

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