Question

Copy the grid system shown on the previous page onto a piece of graph paper. Then locate the following points.

a. A point$\mathit{T}$five blocks due west of the centre of town.

b. A point$\mathit{U}$five blocks east and two blocks south of the centre of town

c. A point$\mathit{V}$ two blocks west and one block north of your house, which is located at point$\mathit{P}$

Short answer

Points $T$, $U$and $V$are located in the following graph

Step-by-step solution

Part a. Step 1 - Directions on grid system

If centre of the town is at the origin then

• east side is towards positive$x\text{-axis}$
• west side is towards negative$x\text{-axis}$
• north side is towards positive$y\text{-axis}$
• south side is towards negative$y\text{-axis}$

Part a. Step 2 - Find coordinate of point T

As the point is 5 units towards negative $x\text{-axis}$, so its coordinate is$\left(-5,0\right)$

Part a. Step 3 - Plot the point

To show point$T\left(-5,0\right)$ on coordinate grid mark the dot as shown below

Part b. Step 1 - Directions on grid system

If centre of the town is at the origin then

• east side is towards positive$x\text{-axis}$
• west side is towards negative$x\text{-axis}$
• north side is towards positive$y\text{-axis}$
• south side is towards negative$y\text{-axis}$

Part b. Step 2 - Find coordinate of point U

As the point is 5 units towards positive$x\text{-axis}$ and 2 units towards negative $y\text{-axis}$, so its coordinate is$\left(5,-2\right)$

Part b. Step 3 - Plot the point

To show point $U\left(5,-2\right)$on coordinate grid mark the dot as shown below

Part c. Step 1 - Directions on grid system

If centre of the town is at the origin then

• east side is towards positive$x\text{-axis}$
• west side is towards negative$x\text{-axis}$
• north side is towards positive$y\text{-axis}$
• south side is towards negative$y\text{-axis}$

Part c. Step 2 - Find coordinate of point V

As the point is 2 units towards negative $x\text{-axis}$and 1 unit towards positive $y\text{-axis}$from point $P$, so subtract 2 from role="math" localid="1649247675927" $x\text{-coordinate}$and add 1 in $y\text{-coordinate}$of point $P$to get,

$\begin{array}{rcl}\left(3,2\right)+\left(-2,1\right)& =& \left(3-2,2+1\right)\\ & =& \left(1,3\right)\end{array}$

Part c. Step 3 - Plot the point

To show point $V\left(1,3\right)$on coordinate grid mark the dot as shown below