Final answer:
To find the distance between the subway stop at (-5, 1) and your house at (-8, 7), calculate the difference in x and y coordinates, then apply the Pythagorean theorem, resulting in a distance of 3√5 in simplest radical form.
Step-by-step explanation:
The distance between your house and the subway stop can be calculated using the Pythagorean theorem, which applies to finding the distance between two points on a coordinate grid, also known as the Euclidean distance. Since the subway stop is at (–5, 1) and your house at (–8, 7), we calculate the differences in the x-coordinates and y-coordinates separately and then apply the theorem.
The difference in the x-coordinates (x) is: –8 – (–5) = –8 + 5 = –3.
The difference in the y-coordinates (y) is: 7 – 1 = 6.
Now, the Euclidean distance (d) is given by the formula:
d = √(x2 + y2)
So, applying the values we get:
d = √((-3)2 + (6)2)= √(9 + 36)= √45
= 3√5 (in simplest radical form)
Therefore, the distance between the subway stop and your house is 3√5 units in simplest radical form.