Question

Pls help !!!!

Answer 1

Answer:

At any given moment, the red ant's coordinates may be written as (a, a) where a > 0. The  red ant's distance from the anthill is $a\sqrt{2}$ . The black ant's coordinates may be written  as (-a, -a) and the black ant's distance from the anthill is $a\sqrt{2}$  . This shows that at  any given moment, both ants are  $a\sqrt{2}$ units from the anthill.

Step-by-step explanation:

Given:

red ant's coordinates written as (a,a)

black ant's coordinates are written  as (-a, -a)

To find:

The distance of red and black ants from anthill

Solution:

Compute the distance of red ant from the anthill using distance formula

d (red ant) = $\sqrt{(a-0)^{2}+ (a-0)^{2}}$

                 = $\sqrt{a^{2} + a^{2} }$

                 = $\sqrt{2a^{2} }$

                 = $a\sqrt{2}$

So distance of red ant from anthill is $a\sqrt{2}$

Compute the distance of black ant from the anthill using distance formula

d (black ant) = $\sqrt{(-a-0)^{2}+ (-a-0)^{2}}$

                    = $\sqrt{(-a)^{2} + (-a)^{2} }$

                    = $\sqrt{a^{2} + a^{2} }$

                 = $\sqrt{2a^{2} }$

                 = $a\sqrt{2}$

So distance of black ant from anthill is $a\sqrt{2}$

Hence both ants are $a\sqrt{2}$   units from the anthill.