Help with: One diagonal of a square has endpoints (1,2) and (7,10)....

[BenCurtis]

One diagonal of a square has endpoints (1,2) and (7,10). Find the coordinates of the endpoints of the other diagonal.

 

[JeffM]

One diagonal of a square has endpoints (1,2) and (7,10). Find the coordinates of the endpoints of the other diagonal.

Again we do not know what you have done.

What are the names of your unknowns?

What do you know from the givens in the problem?

 

[mmm4444bot]

Where are you stuck, in this exercise?

Do you know how to find the midpoint coordinates, on the given diagonal?

Can you write the equation of the perpendicular line passing through the midpoint?

The other two vertex points lie on this perpendicular line...

 

[soroban]

Hello, BenCurtis!

\(\displaystyle \text{One diagonal of a square has endpoints A(1,2) and C(7,10). }\)
\(\displaystyle \text{Find the coordinates of the endpoints of the other diagonal.}\)

Did you make a sketch?

      |           (7,10)
    10+  Do - - - - ♥C
      |   :       * :
      |   :     *   :
      |   :   *     :
      |   : *       :
     2+  A♥ - - - - oB
      | (1,2)
      |
  - - + - + - - - - + - - -
      |   1         7

Can you guess where points B and D are?

 

[HallsofIvy]

Perpendicular bisector.