Q6. - Geometry

Question

A point is given in the distance-angle system. What would it be called, approximately, in the grid system? (Hint: Use a protractor and a centimetre ruler to draw the triangle suggested by the angle and distance. Measure the sides of the triangle.)

$\mathrm{a}.\left(2,50°\right), \mathrm{b}.\left(1.5,-70°\right), \mathrm{c}.\left(3,90°\right), \mathrm{d}.\left(1,120°\right)$

Step-by-Step Solution

Answer

Given points in distance-angle system be called as

$\mathrm{a}.\left(1.28,1.58\right), \mathrm{b}.\left(0.51,-1.41\right), \mathrm{c}.\left(0,3\right)\text{, }\mathrm{d}.\left(-0.5,0.86\right)$

Part a. Step 1. Plot the point.

Plot the point $\left(2,50°\right)$ on grid system as 2 cm from origin at an angle of $50°$ anticlockwise. 

Part a. Step 2. Find grid system point.

Use a protractor and a centimetre ruler to draw the triangle as shown in the figure then measure the sides of triangle.

 $\begin{array}{l}x=1.28\text{ cm}\\ y=1.58\text{ cm}\end{array}$

Part a. Step 3. Write given point in grid system.

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

Thus, $\left(2,50°\right)=\left(1.28,1.58\right)$

Part b. Step 1. Plot the point.

Plot the point $\left(1.5,-70°\right)$ on grid system as $1.5$ cm from origin at an angle of $70°$ clockwise.

Part b. Step 2. Find grid system point.

Use a protractor and a centimetre ruler to draw the triangle as shown in the figure then measure the sides of triangle.

$\begin{array}{l}x=0.51\text{ cm}\\ y=-1.41\text{ cm}\end{array}$

Part b. Step 3. Write given point in grid system.

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

Thus, $\left(1.5,-70°\right)=\left(0.51,-1.41\right)$

Part c. Step 1. Plot the point.

Plot the point $\left(3,90°\right)$ on grid system as 3 cm from origin at an angle of $90°$ anticlockwise. 

Part c. Step 2. Find grid system point.

Use a protractor and a centimetre ruler to draw the triangle as shown in the figure then measure the sides of triangle.

 $\begin{array}{l}x=0\text{ cm}\\ y=3\text{ cm}\end{array}$

Part c. Step 3. Write given point in grid system.

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

Thus, $\left(3,90°\right)=\left(0,3\right)$

Part d. Step 1. Plot the point.

Plot the point $\left(1,120°\right)$ on grid system as 1 cm from origin at an angle of $120°$ anticlockwise. 

Part d. Step 2. Find grid system of point.

Use a protractor and a centimetre ruler to draw the triangle as shown in the figure then measure the sides of triangle.

 $\begin{array}{l}x=-0.5\text{ cm}\\ y=0.86\text{ cm}\end{array}$

Part d. Step 3. Write given point in grid system.

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

Thus, width="156" style="max-width: none; vertical-align: -4px;" $\left(1,120°\right)=\left(-0.5,0.86\right)$