Lesson 11 Plane Geometry Practice Understanding

Ready

Examine each of the scatterplots shown. If possible, make a statement about the relationship between the two quantities depicted in the scatterplot.

1.

2.

3.

4.

The equations for the regression lines for scatterplots 1, 2, and 3 are given in random order. Use what you know about equations of lines to match each equation with the correct scatterplot. Justify your answers.

$y = 4.04481 x - 158.74$
$y = - 0.02488 x + 69.3765$
$y = 3.7 x - 61.357$

Set

Given: $\vec{u} : ⟨ - 5, 1 ⟩$ , $\vec{v} : ⟨ 3, 5 ⟩$ , $\vec{w} : ⟨ 4, - 3 ⟩$ . Each of these three vectors represents a force pulling on an object—such as in a three-way tug-of-war with the force exerted in each direction being measured in pounds.

5.

Find the magnitude of each vector. This is the number of pounds of force being exerted on the object by each tug. (Round to the nearest hundredth.)

a.

$‖ \vec{u} ‖$

b.

$‖ \vec{v} ‖$

c.

$‖ \vec{w} ‖$

6.

$‖ \vec{u} + \vec{v} + \vec{w} ‖$

7.

Draw a vector diagram showing the resultant direction and magnitude of the motion resulting from this three-way tug-of-war.

8.

Consider the effects of the forces if they are multiplied or scaled.

a.

Find the magnitude of $‖ 3 \vec{v} ‖$ .

b.

Find the magnitude of $‖ 2 \vec{w} ‖$ .

c.

Write the component notation and also graph $5 \vec{u}$ .

Go

Show how this system of equations can be solved in three different ways.

${\begin{cases} 4 x - 4 y = 7 \\ 6 x - 8 y = 9 \end{cases}$

9.

First Method:

10.

Second Method:

11.

Third Method: