Question

James is the fire chief. He is planning theemergency route to the hospital from thelocal middle school on the coordinateplane. He uses the axes to represent north(N), south (S), east (E), and west (W). Eachunit on the graph represents one block.James places an orange dot to representthe middle school at (-2,-5). The hospital is8 blocks north and 7 blocks east of theschool. Drag and drop the purple dot to thelocation that James should place thehospital.

Answer 1

To answer this question, we already know that the middle school is represented by an orange dot at (-2, -5).

If we have that the hospital is 8 blocks north (and each unit of the graph represents one block), then we have to add 8 units to the current position in the y-direction - we need to move 8 units up from the current position. We also know that if the hospital is 7 blocks east (we need to move 7 units to the right from the current position in the x-direction).

Now, we can graph the coordinates as follows:

We can solve this situation algebraically if we know that the hospital is 8 blocks north. This is in the y-direction and it is 8 positive units. Likewise, if the hospital will be 7 blocks east, they are 7 positive units in the x-direction. Therefore, we have:

`\begin{gathered} (x,y)\rightarrow(x+7,y+8)\rightarrow(x^(\prime),y^(\prime))_{} \\ (-2,-5)\rightarrow(-2+7,-5+8)\rightarrow(5,3) \end{gathered}`

Therefore, the hospital will be located at the point (5, 3) in the coordinate plane.

In summary, the hospital will be at the coordinates (5, 3) - the purple dot that James should place the hospital in the coordinate plane.