Question

Annabelle the ant and Archibald the ant are on a large coordinate grid. Annabelle is at (3,4) and Archibald is at (33,44). If both ants skate directly towards each other, starting at the same time and skating the same speed, what will be the coordinates of their meeting place?
How far will each ant skate?

Answer 1

Part a) If both ants skate directly towards each other, starting at the same time and skating the same speed, what will be the coordinates of their meeting place?

Let

A(3,4)  B(33.44)

we know that

If both ants skate directly towards each other, starting at the same time and skating the same speed

then

the coordinates of their meeting place is the midpoint AB

Find the midpoint AB

in the x-coordinate

(3+33)/2=18

in the y-coordinate

(4+44)/2=24

the midpoint AB is (18,24)

therefore

the answer Part a) is

the coordinates of their meeting place is (18,24)

Part b) How far will each ant skate?

Find the distance AB

$d=\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}$

substitute the values

$dAB=\sqrt{(33-3)^{2}+(44-4)^{2}}$

$dAB=\sqrt{2,500}$ units

$dAB=50$ units

Find the half distance AB

50/2=25 units

therefore

the answer part b) is

Each ant will skate 25 units