Distance from point to point. X-Y axis

Question

Let’s assume for a moment that we are standing at the origin and the positive y-axis points due North while the positive x-axis points due East. Our Sasquatch-o-meter tells us that Sasquatch is 6 miles West and 7 miles North of our current position. What are the coordinates of his position? How far away is he from us? If he runs 8 miles due East, what would his new position be?

Answer 1

I would suggest starting out by drawing a coordinated system on a piece of graph paper. Label the positive y-axis as North, therefore the negative y-axis is South. Then label the positive x-axis as East, therefore the negative x-axis is West. 

 

So, points in the four quadrants are:

Quadrant I (East, North) or (x,y)

Quadrant II (West, North) or (-x,y)

Quadrant III (West, South) or (-x,-y)

Quadrant IV (East, South) or (x,-y)

 

Part 1) Use this to find the coordinates of the Sasquatch. Hint: The Sasquatch is in quadrant II.

 

Part 2) The distance formula between two points is d = √((x₂ - x₁)² + (y₂ - y₁)²)

 

You are at the origin so your coordinates are (0,0). I would make these coordinates (x₁,y₁). Then make the coordinates of the Sasquatch (x₂,y₂). Then plug these into the distance formula. Remember units are in miles.

 

Part 3) Finally, the Sasquatch runs 8 miles East from his position 6 miles West. He is initially at a -x location and is running towards +x. So just add the x coordinate with the appropriate negative or positive sign to 8 miles since he is running in the positive x direction.