Question

Farley is training for a bike-a-thon. The path he rides, in miles each day, is represented by the rectangle in the coordinate plane below.

On a coordinate plane, points are at (negative 4, 3), (negative 4, 0), (4, 0), and (4, 3).

How far does Farley ride each day?
8 miles
11 miles
16 miles
22 miles

Answer 1

it is 22 miles

Step-by-step explanation:

did the quiz

Answer 2

Farley rides 22 miles each day .

Explanation:

Let us take the 4 points as A(-4,3), B (-4,0), C (4,0) and D (4,3).

Let us consider that each unit on a plane is 1 mile. So in order to calculate how far did Farley rode, we need to calculate all the 4 distances, which are A to B, B to C, C to D, and D to A.

Distance between two points P(x1,y1) and Q(x2,y2) is given by:

d (P, Q) =
`\sqrt{(x_2-x_1)^(2) + (y_2-y_1)^(2)}`

Distance A to B:

We need to calculate the distance between these two coordinates (-4,3) and (-4,0).

d (A, B) =
`\sqrt{(-4-(-4))^(2) + (0-(-3))^(2)}`

d (A, B) =
`\sqrt{(-4+4))^(2) + (0+3))^(2)}`

d (A, B) =
`\sqrt{(0)^(2) + (3)^(2)}`

d (A, B) =
`\sqrt{(3)^(2)}`

d (A, B) =
`√((9))`

d (A, B) = 3

Distance B to C:

We need to calculate the distance between these two coordinates (-4,0) and (4,0).

d (B, C) =
`\sqrt{(4-(-4))^(2) + (0-0)^(2)}`

d (B, C) =
`\sqrt{(4+4))^(2) + (0))^(2)}`

d (B, C) =
`\sqrt{(8)^(2) + (0)^(2)}`

d (B, C) =
`\sqrt{(8)^(2)}`

d (B, C) =
`√((16))`

d (B, C) = 8

Distance C to D:

We need to calculate the distance between these two coordinates (4,0) and (4,3).

d (C, D) =
`\sqrt{(4-(4))^(2) + (3-0)^(2)}`

d (C, D) =
`\sqrt{(0))^(2) + (3))^(2)}`

d (C, D) =
`√((0) + (9))`

d (C, D) =
`√((9))`

d (C, D) = 3

Distance D to A:

We need to calculate the distance between these two coordinates (4,3) and (-4,3).

d (D, A) =
`\sqrt{(-4-(4))^(2) + (3-3)^(2)}`

d (D, A) =
`\sqrt{(-8))^(2) + (0))^(2)}`

d (D, A) =
`√((64) + (0))`

d (D, A) =
`√((64))`

d (D, A) = 8

Farley's daily distance = d (A, B) + d (B, C) + d (C, D) + d (D, A) = 3 + 8 + 3 + 8 = 22 miles.