Write the coordinates of the fourth vertex of a square?
Answers
Step-by-step explanation:
vertex are (1,-2).
Step-by-step explanation:
Consider the given vertices of square are A(1,2), B(5,2), C(5,-2).
We know that diagonals of a square are perpendicular bisector. So, midpoint of both diagonals are same.
Let the coordinate of the fourth vertex are D(a,b).
Midpoint of BD = Midpoint of AC
(\dfrac{5+a}{2},\dfrac{2+b}{2})=(\dfrac{1+5}{2},\dfrac{2-2}{2})(
2
5+a
,
2
2+b
)=(
2
1+5
,
2
2−2
)
(\dfrac{5+a}{2},\dfrac{2+b}{2})=(3,0)(
2
5+a
,
2
2+b
)=(3,0)
On comparing both sides.
\dfrac{5+a}{2}=3
2
5+a
=3
5+a=65+a=6
a=6-5=1a=6−5=1
The value of a is 1.
\dfrac{2+b}{2}=0
2
2+b
=0
2+b=02+b=0
b=-2b=−2
The value of b is -2.
Therefore, the coordinate of the fourth vertex are (1,-2).
#Learn more
(2,1),(-1,2) and (1,0) are the coordinates of three vertices of a parallelogram.Find the fourth vertex
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