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

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) = $\sqrt{(9)}$

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) = $\sqrt{(16)}$

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) = $\sqrt{(0) + (9)}$

d (C, D) = $\sqrt{(9)}$

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) = $\sqrt{(64) + (0)}$

d (D, A) = $\sqrt{(64)}$

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.