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The line 3x + 2y = 6 will divide the quadrilateral formed y the lines x + y = 5, y – 2x = 8, 3y + 2x = 0 & 4y – x = 0 in
- a)Two quadrilaterals
- b)One pentagon and one triangle
- c)Two triangles
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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The line 3x + 2y = 6 will divide the quadrilateral formed y the lines ...
In order to determine whether the line 3x + 2y = 6 will divide the quadrilateral formed by the lines x + y = 5, y = 3, x = 2, and y = 0, we need to find the points of intersection between the lines.
First, let's find the intersection between the lines x + y = 5 and y = 3:
x + y = 5
x + 3 = 5
x = 2
So the first point of intersection is (2, 3).
Next, let's find the intersection between the lines x = 2 and y = 0:
x = 2
y = 0
So the second point of intersection is (2, 0).
Now let's find the intersection between the lines y = 3 and y = 0:
y = 3
y = 0
Since the y-values are different, these lines do not intersect.
Finally, let's find the intersection between the lines 3x + 2y = 6 and y = 0:
3x + 2y = 6
3x + 2(0) = 6
3x = 6
x = 2
So the third point of intersection is (2, 0).
Now we can plot these points on a graph:
(2, 3) is the top right corner of the quadrilateral.
(2, 0) is the bottom right corner of the quadrilateral.
To determine the remaining corners of the quadrilateral, we can substitute the x-values of the points of intersection into the equation x + y = 5:
For (2, 3):
2 + y = 5
y = 3
So the top left corner of the quadrilateral is (0, 3).
For (2, 0):
2 + y = 5
y = 3
So the bottom left corner of the quadrilateral is (0, 3).
Now we can draw the quadrilateral on the graph:
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0 1 2 3 4 5 x
Since the line 3x + 2y = 6 passes through the points (2, 3) and (2, 0), it does not divide the quadrilateral formed by the lines x + y = 5, y = 3, x = 2, and y = 0.
First, let's find the intersection between the lines x + y = 5 and y = 3:
x + y = 5
x + 3 = 5
x = 2
So the first point of intersection is (2, 3).
Next, let's find the intersection between the lines x = 2 and y = 0:
x = 2
y = 0
So the second point of intersection is (2, 0).
Now let's find the intersection between the lines y = 3 and y = 0:
y = 3
y = 0
Since the y-values are different, these lines do not intersect.
Finally, let's find the intersection between the lines 3x + 2y = 6 and y = 0:
3x + 2y = 6
3x + 2(0) = 6
3x = 6
x = 2
So the third point of intersection is (2, 0).
Now we can plot these points on a graph:
(2, 3) is the top right corner of the quadrilateral.
(2, 0) is the bottom right corner of the quadrilateral.
To determine the remaining corners of the quadrilateral, we can substitute the x-values of the points of intersection into the equation x + y = 5:
For (2, 3):
2 + y = 5
y = 3
So the top left corner of the quadrilateral is (0, 3).
For (2, 0):
2 + y = 5
y = 3
So the bottom left corner of the quadrilateral is (0, 3).
Now we can draw the quadrilateral on the graph:
| .
| .
| .
| .
+-------------------
0 1 2 3 4 5 x
Since the line 3x + 2y = 6 passes through the points (2, 3) and (2, 0), it does not divide the quadrilateral formed by the lines x + y = 5, y = 3, x = 2, and y = 0.
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The line 3x + 2y = 6 will divide the quadrilateral formed y the lines x + y = 5, y –2x = 8, 3y + 2x = 0 & 4y –x = 0 ina)Two quadrilateralsb)One pentagon and one trianglec)Two trianglesd)None of theseCorrect answer is option 'A'. Can you explain this answer?
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