Question

1In 33-37, use the coordinate planeat the right33. What is located at (0.5, -0.5)?ParrotLake34. What is located at (-1.3)?MysteryMountain35. Write the ordered pair to locateBrown Bat CaveOld OakTree36. Higher Order Thinking Suppose +marks the spot where the treasure isburied. Explain the shortest route,using grid lines as units, from Pirate'sCove to the treasure,Pirate'sCoveRed RockCanyonBrownBat Cave37. Which two locations are reflections of each other acrossone or both of the axes of the coordinate plane?

Answer 1

We know that the 'x' coordinate represents the perpendicular distance from y-axis, and the 'y' coordinate represents the perpendicular distance from x-axis.

It can also be visualized that (x,y) is a point obtained by moving x units horizontally, and then y units vertically, with respect to the origin.

In the given graph, it is observed that on the x-axis 1 and -1 are marked at 10 grid lines, so the length that each grid step represents is calculated as,

`\begin{gathered} =(1)/(10) \\ =0.1 \end{gathered}`

So we found that each step represents 0.1 units.

33.

Consider the given coordinate (0.5,-0.5).

In order to reach this point, move 5 steps right and then 5 steps down. We see that this is the location of Red Rock Canyon.

Thus, Red Rock Canyon is located at (0.5,-0.5).

34.

Consider the given coordinate (-1/2 , 2/5) i.e. (-0.5 , 0.4)

In order to reach this point, move 5 steps left and then 4 steps up. We see that this is the location of Mystery Mountain.

Thus, Mystery Mountain is located at (-0.5 , 0.4).

35.

Consider the location of Brown Bat Cave.

It is situated at distance 8 steps on the right, and 7 steps down.

So it's location can be represented by the coordinate (0.8,-0.7) .

36.

Given that the origin is the location of the treasure.

The Pirate's cove is 7 steps left and 6 steps down. The shortest distance from this point to the treasure will be equal to the hypotenuse of the right triangle with base 0.7 units and height 0.6 units.

Solve for the hypotenuse (H) using Pythagoras Theorem as follows,

`\begin{gathered} H^2=0.7^2+0.6^2 \\ H^2=0.49+0.36 \\ H^2=0.85 \\ H=\sqrt[]{0.85} \\ H\approx0.922 \end{gathered}`

Thus, the treasure is approximately 0.922 units from the Pirate's Cove.

37.

Consider that the reflection about origin is characterized as,

`(x,y)\rightarrow(-x,-y)`

The location of Parrot's lake is (-5,5) while the Red Rock Canyon is located at (5,-5).

Both these points satisfy the condition of reflection.

So they will be the image of each other, while considering the reflection about the origin.

Thus, the required locations are Parrot's lake and Red Rock Canyon .