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| PAGE: 352 | SET: Exercises | PROBLEM: 6 |
Explore: Plot the vertices on a coordinate plane.
Plan:
If the diagonals are perpendicular, then ABCD is either a rhombus or a square.
The diagonals of a rectangle are congruent. If the diagonals are congruent and perpendicular, then ABCD is a square.
,N(-3,0),P(0,-3),Q(3,0).gif)
Solve:
Use the Distance Formula to compare the lengths of the diagonals.
The distance formula is 
.
(Substitute 
)
(Simplify)
(Substitute 
)
(Simplify)
Use slope to determine whether the diagonals are perpendicular.
The slope formula is 
.
Slope of 
(Substitute 
)
Slope of 
(Substitute 
)
Since the slope of 
is the negative reciprocal of the slope of 
, the diagonals are perpendicular. 
and 
have the same measure, so the diagonals are congruent. ABCD is a rhombus, a rectangle, and a square. 
ABCD is a rhombus, a rectangle, and a square.
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