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The point (9, 0), (9, 6), (-9, 6) and (-9, 0) are the vertices of a _________.
square
rectangle
trepezium
rhombus
rectangle
Observe the changes in x and y coordinates. Since the x-coordinates change by 18 units and y-coordinates change by 6 units, and the lines are parallel to the axes, the sides are unequal, immediately ruling out a square/rhombus.
Four vertices of a quadrilateral are given as (9, 0), (9, 6), (-9, 6), and (-9, 0).
d=(x2тАЛтИТx1тАЛ)2+(y2тАЛтИТy1тАЛ)2тАЛ
Observe the changes in x and y coordinates. Since the x-coordinates change by 18 units and y-coordinates change by 6 units, and the lines are parallel to the axes, the sides are unequal, immediately ruling out a square/rhombus.
Students often assume any 4-sided figure with 90-degree angles is a square without checking if the length equals the width.
Calculate side lengths
Let the vertices be A(9,0), B(9,6), C(-9,6), and D(-9,0). The length of AB = |6 - 0| = 6 units, and BC = |9 - (-9)| = 18 units.
AB=6,BC=18
Compare adjacent sides
Since length AB (6 units) is not equal to length BC (18 units), the figure cannot be a square or a rhombus.
6юАа=18
Verify shape
Since the vertices form right angles (vertical lines x=9 and x=-9, horizontal lines y=0 and y=6) and opposite sides are equal, it is a rectangle.
Oppositesidesareequalandanglesare90┬░
B is correct because the opposite sides are unequal (6 and 18) but all angles are right angles, which defines a rectangle.
In coordinate geometry, always check if the sides are parallel to the axes by checking constant x or y values; this saves time calculating full distances.
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