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Conics Homework -- Distance

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides practice problems about calculating distance between two points.

Exercise 1

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

Exercise 2

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

Exercise 3

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

Exercise 4

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

Exercise 5

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

Hint:

the answer is not 17 miles. Draw it!

Exercise 6

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

Exercise 7

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

Hint:

think about specific points—such as (4,2) or (1,10)—until you can see the pattern, and answer the question for the general point (xx,yy).

Exercise 8

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

Exercise 9

Find the distance dd from the origin to that point (xx,yy), using the Pythagorean Theorem. This will give you a formula for the distance from any point, to the origin.

Exercise 10

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

Exercise 11

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

Exercise 12

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

Exercise 13

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

Exercise 14

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

Exercise 15

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

Exercise 16

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

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Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

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