Question

Show that the points (1,1),(-1,5),(7,9) and (9,5) taken in order are the vertices of a rectangle​

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

To show that the given points A(1,1), B(-1,5), C(7,9) and D(9,5) are vertexes of a rectangle we have to show, that:

- AB║CD and BC ║ AD (slope of parallel lines are equal) ;

- AB ⊥ BC and CD ⊥ AD ;

$m_{AB}$ = $\frac{5-1}{-1-1}$ = - 2 , $m_{CD}$ = $\frac{5-9}{9-7}$ = - 2

$m_{BC}$ = $\frac{5-9}{-1-7}$ = $\frac{1}{2}$ , $m_{AD}$ = $\frac{5-1}{9-1}$ = $\frac{1}{2}$

Slopes of lines AB and BC are opposite reciprocals, as well as slopes of lines CD and AD.

Thus, ABCD is rectangle.