Q4. - Geometry

Question

Give another way of naming each point.

a. $\left(1,-120°\right)$

b. $\left(2,300°\right)$

c. $\left(2.5,-180°\right)$

Step-by-Step Solution

Answer

Another way of naming each point is

$$\begin{gathered} \mathrm{a}.\left(1,240°\right), \\ \mathrm{b}.\left(2,-60°\right), \\ \mathrm{c}.\left(2.5,180°\right) \end{gathered}$$

Part a. Step 1. Meaning of point.

Negative sign with angle represents clockwise direction whereas positive sign represent anticlockwise direction.

So given point is 1 unit from the origin and makes $120°$ clockwise.

Part a. Step 2. Change the direction of point.

On reversing the direction from clockwise to anticlockwise subtract given angle from $360°$ as shown below

$360°-120°=240°$ 

Part a. Step 3. Write other name of given point.

Given point is represented as 1 unit from the origin and makes $240°$ anticlockwise.

So point is $\left(1,240°\right)$

Part b. Step 1. Meaning of point.

Negative sign with angle represents clockwise direction whereas positive sign represent anticlockwise direction.

So given point is 2 unit from the origin and makes $300°$ anticlockwise.

Part b. Step 2. Change the direction of point.

On reversing the direction from clockwise to anticlockwise subtract given angle from $360°$ as shown below

$360°-300°=60°$ 

Part b. Step 3. Write other name of given point.

Given point is represented as 2 unit from the origin and makes $60°$ clockwise.

So point is $\left(2,60°\right)$

Part c. Step 1. Meaning of point.

Negative sign with angle represents clockwise direction whereas positive sign represent anticlockwise direction.

So given point is $2.5$ unit from the origin and makes $180°$ clockwise.

Part c. Step 2. Change the direction of point.

On reversing the direction from clockwise to anticlockwise subtract given angle from $360°$ as shown below

$360°-180°=180°$

Part c. Step 3. Write other name of given point.

Given point is represented as $2.5$ unit from the origin and makes $180°$ anticlockwise.

So point is $\left(2.5,180°\right)$