Question

Angela uses point (4, 3) to represent the location of her house and uses the point (10, 8) to represent the location of a gas station. Each unit on the graph represents 1 miles. She wants to drive to the gas station using a straight line. How far is the gas station from Angela's house?

Answer 1

7.8 miles

Step-by-step explanation

We have that Angela's house is at point (4, 3) and the gas station is located at (10, 8).

We want to find the straight line distance (in miles) between her house and the gas station.

To do that, we need to find the distance between the two points on the graph.

Since each unit is 1 mile, we then convert the distance (in units) to miles.

The distance between two coordinate points on a graph is given as:

`D\text{ = }\sqrt[]{(x2-x1)^2+(y2-y1)^2}`

where (x1, y1) and (x2, y2) are the two points.

So, we have that:

`\begin{gathered} D\text{ = }\sqrt[]{(10-4)^2+(8-3)^2}=\sqrt[]{6^2+5^2} \\ D\text{ = }\sqrt[]{36\text{ + 25}}\text{ = }\sqrt[]{61} \\ D\text{ = 7.8 units} \end{gathered}`

Therefore, converting to miles:

1 unit = 1 mile

=> 7.8 units = 7.8 miles

Therefore, the gas station is 7.8 miles far from Angela's house.