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Homework: Distance

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

Summary: This module provides homework problems related to finding distance between points.

Exercise 1

Draw a point anywhere. Instead of labeling the specific coordinates of that point, just label it ( x 1 x 1 , y 1 y 1 ).

Exercise 2

Draw another point somewhere else. Label it ( x 2 x 2 , y 2 y 2 ). To make life simple, make this point higher and to the right of the first point.

Exercise 3

Draw the line going from ( x 1 x 1 , y 1 y 1 ) to ( x 2 x 2 , y 2 y 2 ). Then fill in the other two sides of the triangle

Exercise 4

How far up is it from the first point to the second? (As always, start by thinking about specific numbers—then see if you can generalize.)

Exercise 5

How far across is it from the first point to the second?

Exercise 6

Find the distance dd from ( x 1 , y 1 x 1 , y 1 ) to ( x 2 , y 2 x 2 , y 2 ), using the Pythagorean Theorem. This will give you a general formula for the distance between any two points.

Exercise 7

Plug in x 2 = 0 x 2 =0 and y 2 = 0 y 2 =0 into your formula. You should get the same formula you got on the previous assignment, for the distance between any point and the origin. Do you?

Exercise 8

Draw a line from (0,0) to (4,10). Draw the point at the exact middle of that line. (Use a ruler if you have to.) What are the coordinates of that point?

Exercise 9

Draw a line from (–3,2) to (5,–4). What are the coordinates of the midpoint?

Exercise 10

Look back at your diagram of a line going from ( x 1 , y 1 x 1 , y 1 ) to ( x 2 , y 2 x 2 , y 2 ). What are the coordinates of the midpoint of that line?

Exercise 11

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

Exercise 12

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

Exercise 13

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

Exercise 14

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

Exercise 15

Find the coordinates of all the points that have yy-coordinate 5, and which are exactly 10 units away from the origin.

Exercise 16

Draw all the points you can find which are exactly 3 units away from the point (4,5).

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