Question

harper walked from the pet store to the train station and then from the train station to the art gallery. how far did harper walk in all? units

Explanation:

Step1: Find the distance from pet store to train station

The pet store is at \((3,4)\) and the train station is at \((3,5)\). Using the distance formula for vertical distance (since \(x -\)coordinates are same), \(d_1=\vert y_2 - y_1\vert=\vert5 - 4\vert = 1\) unit.

Step2: Find the distance from train station to art gallery

The train station is at \((3,5)\) and the art gallery is at \((4,1)\). Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), here \(x_1 = 3,y_1 = 5,x_2=4,y_2 = 1\). Then \(d_2=\sqrt{(4 - 3)^2+(1 - 5)^2}=\sqrt{1+16}=\sqrt{17}\approx4.12\) (not needed as we can count units on grid). Counting units: 1 unit right (\(x -\)direction) and 4 units down (\(y -\)direction). Total units for this part \(1 + 4=5\) units.

Step3: Calculate total distance

Total distance \(d=d_1 + d_2=1+5 = 6\) units.

Answer:

6