The distance between Angela's house and the gas station, is the distance between the points (4,3) and (10,8). To find that distance, we are going to use the distance formula: [tex]d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex]
From our two points we can infer that [tex]x_1=4[/tex], [tex]y_1=3[/tex], [tex]x_2=10[/tex], and [tex]y_2=8[/tex]. So lets replace those values in our ditance formula:
[tex]d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex]
[tex]d= \sqrt{(10-4)^2+(8-3)^2} [/tex]
[tex]d= \sqrt{(6)^2+(5)^2}[/tex]
[tex]d= \sqrt{36+25}[/tex]
[tex]d= \sqrt{61} [/tex]
We can conclude that the gas station is [tex] \sqrt{61} [/tex] units, which is approximately 7.8 units, from her house.
