Writing Robin's position as parametric equations, we have

From these equations, we see that Robin is moving 8 km right and 6 km up every hour. If Casey is 20 km behind, that means that Casey is 16 km LEFT and 12 km DOWN from Robin and any time. We can write this in two ways (though the first way is preferable):

or

Problem 3

(a) Look at the line y=1.3 or x=10.75 or y=x+7.1

(b) Only if the slope is irrational. For example,

(c) If it passes through two lattice points, the line has a rational slope and will pass through other lattice points.

The vector from A to B is [-5,2]. Finding a vector that starts at C(4,3) and is perpendicular to [-5,2] means I need to step RIGHT 2 units and UP 5 units from C. Therefore, a point P that makes the vector from C to P perpendicular to the vector from A to B is P(6,8). The vector from C to P is [2,5].

Of course, and point on the line through A and P will do.

Problem 7

Problem 8

Begin by trying to complete triangle ADF. Then, place a point at the midpoint of AC. Can you find another triangle that is congruent to ADF?

Problem 9

You have seen this problem before. This is a question of SLOPES! Solve the following proportion for x

Problem 10

C'mon! You try this one. I bet there is something strange waiting to happen.

Problem 11

Try to draw a picture of the cube unfolded.

Problem 12

You need to solve the system shown on the graph above for the coordinates of B. Then you need to find the time t that the bug is at B.

Solving this system, we find x=4.9. Looking at the parametric equations, we see that x(t) = 6-t, so 4.9 = 6 - t, or t=1.1 seconds.

From looking at the applet, it looks as if the paths are parallel. Looking at the parametric equations, both paths have a slope of 2. Also, it looks as if point Q moves much faster than P. Looking at the parametric equations, point Q moves with a speed of

units of distance per unit of time and P moves

units of distance per unit of time, which means Q is moving 3 times as fast.

Page 18

Problem 1

In the fourth line, writing

would have been incorrect because this statement implies that angle ABC is congruent to angle ACD (corresponding parts of congruent triangles are congruent), when angle ABC is actually congruent to angle ADC.

Problem 2

Angle ABC and Angle ADC are congruent by CPCTC (corresponding parts of congruent triangles are congruent). Simply replace the line five in the proof by this statement.

## Table of Contents

## Page 17

## Problem 1

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## Problem 2

Writing Robin's position as parametric equations, we have

From these equations, we see that Robin is moving 8 km right and 6 km up every hour. If Casey is 20 km behind, that means that Casey is 16 km LEFT and 12 km DOWN from Robin and any time. We can write this in two ways (though the first way is preferable):

or

## Problem 3

(a) Look at the line y=1.3 or x=10.75 or y=x+7.1

(b) Only if the slope is irrational. For example,

(c) If it passes through two lattice points, the line has a rational slope and will pass through other lattice points.

## Problem 4

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## Problem 5 and 6

The vector from A to B is [-5,2]. Finding a vector that starts at C(4,3) and is perpendicular to [-5,2] means I need to step RIGHT 2 units and UP 5 units from C. Therefore, a point P that makes the vector from C to P perpendicular to the vector from A to B is P(6,8). The vector from C to P is [2,5].

Of course, and point on the line through A and P will do.

## Problem 7

## Problem 8

Begin by trying to complete triangle ADF. Then, place a point at the midpoint of AC. Can you find another triangle that is congruent to ADF?

## Problem 9

You have seen this problem before. This is a question of SLOPES! Solve the following proportion for

x## Problem 10

C'mon! You try this one. I bet there is something strange waiting to happen.

## Problem 11

Try to draw a picture of the cube unfolded.

## Problem 12

You need to solve the system shown on the graph above for the coordinates of B. Then you need to find the time t that the bug is at B.

Solving this system, we find x=4.9. Looking at the parametric equations, we see that x(t) = 6-t, so 4.9 = 6 - t, or t=1.1 seconds.

## Problem 13

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## Problem 14

From looking at the applet, it looks as if the paths are parallel. Looking at the parametric equations, both paths have a slope of 2. Also, it looks as if point Q moves much faster than P. Looking at the parametric equations, point Q moves with a speed of

units of distance per unit of time and P moves

units of distance per unit of time, which means Q is moving 3 times as fast.

## Page 18

## Problem 1

In the fourth line, writing

would have been incorrect because this statement implies that angle ABC is congruent to angle ACD (corresponding parts of congruent triangles are congruent), when angle ABC is actually congruent to angle ADC.

## Problem 2

Angle ABC and Angle ADC are congruent by CPCTC (corresponding parts of congruent triangles are congruent). Simply replace the line five in the proof by this statement.

## Problem 3