Distance

Draw the points (2,5), (10,5), and (10,1), and the triangle they all form.

Find the distance from (2,5) to (10,5) (just by looking at it).

Find the distance from (10,5) to (10,1) (just by looking at it).

Find the distance from (2,5) to (10,1), using your answers to #2 and #3 and the Pythagorean Theorem.

I start at Raleigh Charter High School. I drive 5 miles West, and then 12 miles North. How far am I now from RCHS?

Draw a point anywhere in the first quadrant. Instead of labeling the specific coordinates of that point, just label it ( $x$ , $y$ ).

How far down is it from your point to the $x$ -axis?

How far across is it from your point to the $y$ -axis?

Find the distance $d$ from the origin to that point ( $x$ , $y$ ), using the Pythagorean Theorem. This will give you a formula for the distance from any point, to the origin.

Find the distance from the point (3,7) to the line $y=2$ .

Find the distance from the generic point ( $x$ , $y$ ) (as before) to the line $y=2$ .

Find the distance from the point (3,7) to the line $y=-2$ .

Find the distance from the generic point ( $x$ , $y$ ) to the line $y=-2$ .

I’m thinking of a point which is exactly 5 units away from the point (0,0). The $y$ -coordinate of my point is 0. What is the $x$ -coordinate? Draw this point.

I’m thinking of two points which are exactly 5 units away from (0,0). The $x$ -coordinates of both points is 4. What are the $y$ -coordinates? Draw these points on the same graph that you did #14.

I’m thinking of two points which are exactly 5 units away from (0,0). The $x$ -coordinates of both points is –4. What are the $y$ -coordinates? Draw these points on the same graph that you did #14.