Question

If A(2, 2), B(6, 4), C(4, 4) and D(8, 6) are four points then prove that: AB= CD ​

Answer 1

THE ONLY WAY WE CAN PROVE THAT AB IS EQUAL CD IS BY CALCULATING THE DISTANCES AND THEN COMPARING THEM.

FOR AB

`= \sqrt{( {x2 - x1})^(2) + ( {y2 - y1})^(2) } \\ = \sqrt{(( {6- 2})^(2) + ( ({4 - 2})^(2) } \\ = \sqrt{( {4})^(2) +( {2})^(2) } \\ = √(16 + 4) \\ = √(20)`

THE DISTANCEAB IS GIVEN ABOVE.

NOW LET US CALCULATE DISTANCE CD

`= \sqrt{ ({8 - 4)}^(2) + ({6 - 4})^(2) } \\ = \sqrt{ {(4})^(2) + ({2})^(2) } \\ = √(16 + 4) \\ = √(20)`

WE CAN SEE THAT DISTANCE AB AND DISTAMCE CD ARE EQUAL THERE SE CAN NOW SAY

AB=CD