ARML Power Round - 1

Algebra Level 2

The Distance Formula in two dimensions is given by:

D = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 D = \sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}

Let the taxicab distance be defined as:

D t = ∣ x 2 − x 1 ∣ + ∣ y 2 − y 1 ∣ D_t = |x_2-x_1|+|y_2-y_1|

What is the taxicab distance between ( 5 , 6 ) (5,6) and ( 1 , 2 ) (1,2) ?

This problem is not original, it comes from ARML 2016 Power Round


The answer is 8.

Alex G by Alex G , 22, USA

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1 solution

Hung Woei Neoh
Jun 5, 2016

D t = ∣ x 2 − x 1 ∣ + ∣ y 2 − y 1 ∣ = ∣ 5 − 1 ∣ + ∣ 6 − 2 ∣ = 4 + 4 = 8 D_t = |x_2 - x_1| + |y_2 - y_1|\\ =|5-1| + |6-2|\\ =4+4\\ =\boxed{8}

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