Q5. - Geometry

Question

A point is given in the grid system. What would it be called in the distance-angle system? (Hint: see the discussion at the top of the page. Use a protractor and a centimetre ruler to help you answer the question.)

$\text{a}.\left(3,4\right),\text{ b}.\left(-2,5\right),\mathrm{c}.\left(4,0\right),\mathrm{d}.\left(8,-6\right)$

Step-by-Step Solution

Answer

Given points in distance-angle system be called as

$\mathrm{a}.\left(5,53.13°\right), \mathrm{b}.\left(5.38,113.08°\right), \mathrm{c}.\left(4,0°\right)\text{, d}.\left(10,-36.86°\right)$

Part a. Step 1. Plot the point.

Plot the point $\left(3,4\right)$ on grid system as 3 cm towards right on x-axis and 4 cm upwards on y-axis.

Part a. Step 2. Find distance-angle of point.

Draw the triangle as shown in the figure then use a protractor and a centimetre ruler to find the angle and distance of the point from origin.

$\begin{array}{l}\text{angle}=53.13°\\ \text{distance}=5\text{ cm}\end{array}$ 

Part a. Step 3. Write given point in distance-angle system.

Conversion of point $\left(x,y\right)$ in distance-angle system is  

Thus,  $\left(3,4\right)=\left(5,53.13°\right)$

Part b. Step 1. Plot the point.

Plot the point $\left(-2,5\right)$ on grid system as 2 cm towards left on x-axis and 5 cm upwards on y-axis. 

Part b. Step 2. Find distance-angle of point.

Draw the triangle as shown in the figure then use a protractor and a centimetre ruler to find the angle and distance of the point from origin.

$\begin{array}{l}\text{angle}=113.08°\\ \text{distance}=5.38\text{ cm}\end{array}$ 

Part b. Step 3. Write given point in distance-angle system.

Conversion of point $\left(x,y\right)$ in distance-angle system is $\left(\text{distance, angle}\right)$ 

Thus, $\left(-2,5\right)=\left(5.38,113.08°\right)$

Part c. Step 1. Plot the point.

Plot the point $\left(4,0\right)$ on grid system as 4 cm towards right on x-axis. 

Part c. Step 2. Find distance-angle of point.

Use a protractor and a centimetre ruler to find the angle and distance of the point from origin.

$\begin{array}{l}\text{angle}=0°\\ \text{distance}=4\text{ cm}\end{array}$ 

Part c. Step 3. Write given point in distance-angle system.

Conversion of point $\left(x,y\right)$ in distance-angle system is  

Thus, $\left(4,0\right)=\left(4,0°\right)$

Part d. Step 1. Plot the point.

Plot the point $\left(8,-6\right)$ on grid system as 8 cm towards right on x-axis and 6 cm downwards on y-axis. 

Part d. Step 2. Find distance-angle of point.

Draw the triangle as shown in the figure then use a protractor and a centimetre ruler to find the angle and distance of the point from origin.

$\begin{array}{l}\text{angle}=-36.86°\\ \text{distance}=10\text{ cm}\end{array}$ 

Part d. Step 3. Write given point in distance-angle system.

Conversion of point $\left(x,y\right)$ in distance-angle system is  

Thus, $\left(8,-6\right)=\left(10,-36.86°\right)$