Question

1. what is the taxicab distance from (2, 3) to the following points?

a. (7, 9)
b. (-3, 8)
c. (2, -1)
d. (6, 5.4)
e. (-1.24, 3)
f. (-1.24, 5.4)

Explanation:

Part (a)

Step1: Recall taxicab distance formula

The taxicab distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(d = |x_2 - x_1|+|y_2 - y_1|\).

Step2: Identify coordinates

Here, \((x_1, y_1)=(2, 3)\) and \((x_2, y_2)=(7, 9)\).

Step3: Calculate differences

\(|x_2 - x_1|=|7 - 2| = 5\) and \(|y_2 - y_1|=|9 - 3| = 6\).

Step4: Sum the absolute differences

\(d=5 + 6=11\).

Part (b)

Step1: Use taxicab distance formula

\(d = |x_2 - x_1|+|y_2 - y_1|\) with \((x_1, y_1)=(2, 3)\) and \((x_2, y_2)=(- 3,8)\).

Step2: Compute absolute differences

\(|x_2 - x_1|=|-3 - 2| = 5\) and \(|y_2 - y_1|=|8 - 3| = 5\).

Step3: Sum the values

\(d = 5+5 = 10\).

Part (c)

Step1: Apply taxicab distance formula

For \((x_1, y_1)=(2, 3)\) and \((x_2, y_2)=(2,-1)\).

Step2: Find absolute differences

\(|x_2 - x_1|=|2 - 2| = 0\) and \(|y_2 - y_1|=|-1 - 3| = 4\).

Step3: Sum the differences

\(d=0 + 4=4\).

Part (d)

Answer:

s:
a. \(\boldsymbol{11}\)
b. \(\boldsymbol{10}\)
c. \(\boldsymbol{4}\)
d. \(\boldsymbol{6.4}\)
e. \(\boldsymbol{3.24}\)
f. \(\boldsymbol{5.64}\)