Question
Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are:
y = x, 3y = x, x + y = 8.
y = x, 3y = x, x + y = 8.
✓
Answer
The system of the given equations is,
y = x
3y = x
x + y = 8
Now, y = x
⇒ x = y
When y = 0, we have
x = 0
When y = -3, we have
x = -3
Thus, we have the following table.
We have, 3y = x
⇒ x = 3y
When y = 0, we have
x = 3 × 0 = 0
When y = -1, we have
y = 3 × (-1) = -3
Thus, we have the following table.
We have, x + y = 6
⇒ x = 8 - y
When y = 4, we have
y = 8 - 4 = 4
When y = 5, we have
y = 8 - 5 = 3
Thus, we have the following table.
Graph of the given system of equations.
From the graph of the three equations, we find that the three lines taken in pairs intersect each other at points A(0, 0), B(4, 4) and C(6, 2).
Hence, the vertices of the required triangle are (0, 0), (4, 4) and (6, 2).
y = x
3y = x
x + y = 8
Now, y = x
⇒ x = y
When y = 0, we have
x = 0
When y = -3, we have
x = -3
Thus, we have the following table.
|
x
|
0
|
-3
|
|
y
|
O
|
-3
|
⇒ x = 3y
When y = 0, we have
x = 3 × 0 = 0
When y = -1, we have
y = 3 × (-1) = -3
Thus, we have the following table.
|
x
|
0
|
-3
|
|
y
|
O
|
-1
|
⇒ x = 8 - y
When y = 4, we have
y = 8 - 4 = 4
When y = 5, we have
y = 8 - 5 = 3
Thus, we have the following table.
|
x
|
4
|
5
|
|
y
|
4
|
3
|
From the graph of the three equations, we find that the three lines taken in pairs intersect each other at points A(0, 0), B(4, 4) and C(6, 2).
Hence, the vertices of the required triangle are (0, 0), (4, 4) and (6, 2).
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