Question

Fill in the blanks using correct alternatives.
(1) Seg AB is parallel to Y-axis and coordinates of point A are (1,3) then co–ordinates of point B can be ........ .
(A) (3,1)
(B) (5,3)
(C) (3,0)
(D) (1,–3)

(2) Out of the following, point ........ lies to the right of the origin on X– axis.
(A) (–2,0)
(B) (0,2)
(C) (2,3)
(D) (2,0)

(3) Distance of point (–3,4) from the origin is ...... .
(A) 7
(B) 1
(C) 5
(D) –5

(4) A line makes an angle of 30° with the positive direction of X– axis. So the slope of the line is .......... .

(A) $\frac{1}{2}$

(B) $\frac{\sqrt{3}}{2}$

(C) $\frac{1}{\sqrt{3}}$

(D) $\sqrt{3}$

Answer 1

(1) Slope of y-axis will be not defined because the denominator will be 0.
Since AB is parallel to y-axis, so the slope will be same.
Let the coordinate of point B be (x, y).
Slope of AB = $\frac{y-3}{x-1}$ = slope of y-axis
Slope of y-axis is not defined as the denominator is 0 so, the denominator of $\frac{y-3}{x-1}$ will also be 0.
So,
$$\begin{gathered} x-1=0 \\ \Rightarrow x=1 \end{gathered}$$
with $x=1$ there is only 1 option that (D).
Hence, the correct answer is option D.

(2) A point lying on the right of the origin on X – axis will have positive x-coordinate and non-zero y-coordinate.
So, among the given points (2, 3) lies on the right of the origin on X – axis.
Hence, the correct answer is option (C).

(3) Let the given point be P(–3,4).
Distance of P(–3,4) from the origin O(0, 0) is
$\sqrt{{\left(0-\left(-3\right)\right)}^2+{\left(0-4\right)}^2}=\sqrt{9+16}=\sqrt{25}=5$
Hence, the correct answer is option (C).

(4) Slope of line will be $\tan 30°=\frac{1}{\sqrt{3}}$
Hence, the correct answer is option (C).