Question

the coordinate plane below represents a parking lot. there is a parked motorcycle located at (100, 150) and a parked truck located at (100, -200). (a) plot points to show the locations of the motorcycle and the truck. (b) write an expression that gives the distance between (100, 150) and (100, -200). first choose the correct form, then fill in the blanks choosing only from the numbers 100, 150, and -200. options: |□| + |□| or |□| - |□| (c) on the graph, 1 unit represents 1 meter. use the answer from part (b) to find the distance between the motorcycle and the truck. □ meters

Explanation:

Part (a)

To plot the motorcycle at \((100, 150)\), move 100 units to the right on the x - axis (since \(x = 100\)) and 150 units up on the y - axis (since \(y=150\)). To plot the truck at \((100, - 200)\), move 100 units to the right on the x - axis (since \(x = 100\)) and 200 units down on the y - axis (since \(y=-200\)). (Since this is a plotting task, the visual plot is done on the given coordinate plane as per the coordinates.)

Part (b)

Step 1: Analyze the coordinates

The two points are \((100,150)\) and \((100, - 200)\). Since the x - coordinates are the same (\(x = 100\) for both), the distance between them is the vertical distance. The vertical distance between two points \((x,y_1)\) and \((x,y_2)\) is given by \(|y_1 - y_2|\) or \(|y_2 - y_1|\), which can also be written as \(|y_1|+|y_2|\) when one \(y\) - value is positive and the other is negative (because the distance from the x - axis to each point is the absolute value of their y - coordinates and we add them since they are on opposite sides of the x - axis).
The y - coordinates are \(150\) and \(-200\). So the distance expression is \(|150|+|- 200|\) (or \(|-200|+|150|\)). So we choose the \(|\square|+|\square|\) form and fill in \(150\) and \(-200\) (or \(-200\) and \(150\)).

Step 2: Confirm the form

Since the x - coordinates are equal, the distance is along the y - axis. The distance from \((100,150)\) to the x - axis is \(|150|\) and from \((100, - 200)\) to the x - axis is \(|-200|\). To find the total distance between the two points, we add these two distances. So the correct form is \(|\boldsymbol{150}|+|\boldsymbol{-200}|\) (or \(|-200|+|150|\)).

Part (c)

Step 1: Calculate the absolute values

We know that \(|150|=150\) and \(|-200| = 200\).

Step 2: Add the absolute values

Now, we add these two values: \(150 + 200=350\).

Part (b) Answer:

The correct form is \(|\boldsymbol{150}|+|\boldsymbol{-200}|\) (or \(|-200|+|150|\))

Part (c) Answer:

\(350\) meters

Answer:

Step 1: Calculate the absolute values

We know that \(|150|=150\) and \(|-200| = 200\).

Step 2: Add the absolute values

Now, we add these two values: \(150 + 200=350\).

Part (b) Answer:

The correct form is \(|\boldsymbol{150}|+|\boldsymbol{-200}|\) (or \(|-200|+|150|\))

Part (c) Answer:

\(350\) meters