3 Mark Question

Question 13 Marks

If ‘a’ is a real number, what is the distance between the Y-axis and the line x = a?

Answer

Equation of Y-axis is x = 0.
Since, ‘a’ is a real number, there are two possibilities.
Case I: a > 0
Case II: a < 0 ∴ Distance between the Y-axis and the line x = a = a-0 = a Since, |a| = a, a > 0
= – a, a < 0
∴ Distance between the Y-axis and the line x = a is |a|.

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Question 23 Marks

In the graph alongside, line LM is parallel to the Y-axis.

i. What is the distance of line LM from the Y-axis?
ii. Write the co-ordinates of the points P, Q and R.
iii. What is the difference between the x co-ordinates of the points L and M?

Answer

i. Distance of line LM from the Y-axis is 3 units.
ii. P(3, 2), Q (3, -1), R(3, 0)
iii. x co-ordinate of point L = 3
x co-ordinate of point M = 3
∴ Difference between the x co-ordinates of the points L and M = 3 – 3
= 0

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Question 33 Marks

2x - y + 1 = 0 is a linear equation in two variables in general form. Let us draw the graph of this equation.

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Question 43 Marks

i. Can we draw a line parallel to the Y – axis at a distance of 2 units from ¡t and to its right?
ii. Will all of the points (2, 10), (2, 8), (2, -) be on that line?
iii. What would be the equation of this line?

Answer

i. Yes.
(2, 10)
This line will pass through the point (2, 0).
(2,8)
ii. Yes.
Here, $x$ co-ordinate of the points $(2,10),(2,8),\left(2,-\frac{1}{2}\right)$ is the same, which is 2 .
$\therefore$ All the above points lie on the same line.
iii. Since, the line is at a distance of 2 units to the right of Y-axis.
a = 2
∴ Equation of the line is x = 2.

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Question 53 Marks

i. Can we draw a line parallel to the X-axis at a distance of 6 unIts from It and below the X-axis?
ii. Will all of the points $(-3,-6),(10,-6),\left(\frac{1}{2},-6\right)$ be on that line?
iii. What would be the equation of this line?

Answer

i. Yes.
This line will pass through the point (0,-6).
ii. Yes.
Here, $y$ co-ordinate of the points $(-3,-6),(10,-6),\left(\frac{1}{2},-6\right)$ is the same, which is -6 .
$\therefore$ All the above points lie on the same line.
iii. Since, the line is at a distance of 6 units below the X-axis.
∴ b = -6
∴ Equation of the line is y = -6.

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