Question

Q1.Select the proper option:
The distance between (1.0) and (2, 0) is
(a)
(b) 2
The point on x-axis with the distance 5 units from
(a) (-1.0) (b) (-3,0) (c) (5,0)
The mid-point of a line segment divides it in the rat
(a) 1:2 (b) 2:
(c) 1:1
The distance from the rigin of a point (a, b) is
(a) a2 +62 (6) a_62
(c)​

Answer 1

Step-by-step explanation:

Answer:

Q1.

$\boxed{\bf{ \textbf{Distance Formula} = \sqrt{ (x_2 - x_1)^2 + (y_2-y_1)^2}}} </p><p>$

The values are:

x₁ = 1, x₂ = 2, y₁ = 0, y₂ = 0

Substituting the values in the formula we get:

$\begin{gathered}\implies \text{Distance} = \sqrt{ (2 - 1)^2 + (0-0)^2}\\\\\\\implies \text{Distance} = \sqrt{1 + 0} = \sqrt{1} = 1\end{gathered}$

Hence the distance between the points (1,0) and (2,0) is 1 unit.

Q2.

Since the point is on the x-axis, the value of 'x' would be finite. Also, since it lies entirely on the axis, the value of ordinate or 'y' value in the coordinate would be zero.

Now it is given that the point is 5 units from the y-axis. So, the value of abscissa or 'x' value in the coordinates would be 5.

Therefore the point is (5,0).

Q3.

A midpoint is a geometrical place where the plane/line passing through this points cuts the other line into two equal parts. Since the other two parts are equal their ratio would be 1:1.

Therefore the required ratio is 1:1.

Q4.

Origin = (0,0)

Point = (a,b)

Using the distance formula mentioned in Q1, we get:

$\begin{gathered}\implies \text{Distance} = \sqrt{ (0-a)^2 + (0-b)^2}\\\\\\\implies \text{Distance} = \sqrt{ (-a)^2 + (-b)^2}\\\\\\\implies \boxed{ \bf{\textbf{Distance} = \sqrt{a^2 + b^2}}}\end{gathered}$

These are the required answers.

Answer 2

Answer:

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