I've gotten to the point where I have the following equation: 2 x 2 x...

Sam Hardin

Sam Hardin

Answered

2022-07-04

I've gotten to the point where I have the following equation:
2 x 2 x m 2 x m x 1 + 2 y 2 y m 2 y m y 1 = x 2 2 x 1 2 + y 2 2 y 1 2
Would it be mathematically correct to split this into the following two equations
{ 2 x 2 x m 2 x m x 1 = x 2 2 x 1 2 2 y 2 y 2 2 y m y 1 = y 2 2 y 1 2
and treat them as a system of equations? If so, then how would I go about doing this?

Answer & Explanation

Mateo Carson

Mateo Carson

Expert

2022-07-05Added 15 answers

Step 1
You can not split this equation. That would be the same as saying a + b = c + d can be split into a = c and b = d .
If the points are P 1 , P 2 , and P m , for P m to be the midpoint between P 1 and P 2 , then one way of writing this is that P m must be on the line between P 1 and P 2 (i.e., P m = t P 1 + ( 1 t ) P 2 for 0 t 1 ) and P m must be at the halfway position (i.e., t = 1 2 ).
Another way is that | P 1 P m | = | P 2 P m | and | P 1 P m | = | P 2 P 1 | / 2 . This way gives you two equations for the two unknowns of the x and y components of P m .

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