Find area of square formed by lines
y=x+1, y=x-1,
y=-x+1, y=-x-1 on basis of graph
Answers
Answer:
ho
Step-by-step explanation:
The equation of the given lines are
y−x=0....(1)
x+y=...(2)
x−k=0...(3)
The point of intersection of lines (1) and (2) is given by
x=0 and y=0
The point of intersection of lines (2) and (3) is given by
x=k and y=−k
The point of intersection of lines(3) and (1) is given by
x=k and y=k
Thus, the vertices of the triangle formed by the three given lines are (0,0),(k,−k), and (k,k)
We know that the area of the triangle whose vertices are (x
1
,y
1
),(x
2
,y
2
), and (x
3
,y
3
) is
2
1
∣x
1
(y
2
−y
3
)+x
2
(y
3
−y
1
)+x
3
(y
1
−y
2
)∣
Therefore, area of the triangle formed by the three given lines,
=
2
1
∣0(−k−k)+k(k−0)+k(0+k)∣square unts
=
2
1
∣
∣
∣
k
2
+k
2
∣
∣
∣
square units
=
2
1
∣
∣
∣
2k
2
∣
∣
∣
=k
2
square units
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