Question

Shade the triangle formed by the graphs of 2x−y=2,x+y=1 and y-axis. Write the coordinates of vertices of the triangles ans fatt plsssssssss

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Step-by-step explanation:

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CBSE

Mathematics

Grade 11

Straight Lines in Coordinate Geomet...

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Shade the region formed by the graph of 2x – y = 4, x + y = 2 and the y-axis. Write the coordinates of the vertices of the figure obtained.

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Hint: To solve this question, we will first draw the graph of 2x–y=4 and similarly separate draw the graph of x+y=2 and then join these two with the y-axis. We will form a figure and then try to determine the coordinates of the points obtained.

Complete step-by-step solution:

Let us first consider, 2x–y=4, and draw its graph.

When x=0, we get,

2×0−y=4

⇒y=−4

Therefore, x=0,y=–4.

And when we put y=0, we get,

2x=4

⇒x=42=2

Therefore, x=2,y=0.

So, we have, (0,–4) and (2,0) as the coordinates. So, we will draw the line 2x–y=4 using the coordinates (0,–4) and (2,0).

Similarly, we will draw the line x+y=2. When x=0,y=2. Therefore, the coordinates we get is (0, 2) is a point on the line x+y=2. And when y=0,x=2, so (2,0) is also a point on the line x+y=2.

Let us draw the line x+y=2 using the coordinates (0,2) and (2,0). We have,

Now, let us mix the graphs of 2x–y=4 and x+y=2 and the y-axis, all together to form a triangle. Doing so, we will get,

The shaded region is the required figure obtained. Let the vertices be A, B, and C of the triangle formed. Then as observed by the figure, A=(0,2),B=(2,0), and C=(0,–4) and thus the vertices of the figure are obtained.

Note: If in this question, we were given to take the x-axis apart from the y-axis, then we will need one more information that is exactly which part of the x-axis. The part having a positive y-axis or the part having a negative y-axis. So, always remember to check which axis is given.