Plot the points P (-3, 1) and Q (2, 1) in a rectangular coordinate system and find alle
coordinates of other two vertices of a square having P and Q as two adjacent vertices.
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Answer:
In this case it is a good idea to draw a quick sketch so that you can see what you are dealing with.
Step-by-step explanation:
We can use Pythagoras to solve this as appropriately projecting lines from any point will form a triangle. The vertical and horizontal lengths of which can be read of from the axis.
The distance between two points is
√
(
x
1
−
x
2
)
2
+
(
y
1
−
y
2
)
2
Let the distance between two points be
d
i
Distance between points A and B
d
1
=
√
[
3
−
(
−
3
)
]
2
+
[
7
−
5
]
2
d
1
=
√
36
+
4
=
√
2
2
×
10
=
2
√
10
Distance between points B and C
d
2
=
√
[
6
−
3
]
2
+
[
7
−
(
−
2
)
]
2
d
2
=
√
9
+
81
=
√
3
2
×
10
=
3
√
10
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Area
=
d
1
×
d
2
=
2
√
10
×
3
√
10
=
60
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