2.1 The rectangular coordinate systems and graphs  (Page 6/21)

$4x-3=2y$

$3x+8y=9$

$2x-\frac{2}{3}=\frac{3}{4}y+3$

$4x+2y=8$

$3x-2y=6$

$2x=5-3y$

$x-2y=7$

$5y+4=10x$

$5x+2y=0$

$(\mathrm{-4},1)$ and $(3,\mathrm{-4})$

$(2,\mathrm{-5})$ and $(7,4)$

$(5,0)$ and $(5,6)$

$(\mathrm{-4},3)$ and $(10,3)$

Find the distance between the two points given using your calculator, and round your answer to the nearest hundredth.

$(19,12)$ and $(41,71)$

$(\mathrm{-5},\mathrm{-6})$ and $(4,2)$

$(\mathrm{-1},1)$ and $(7,\mathrm{-4})$

$(\mathrm{-5},\mathrm{-3})$ and $(\mathrm{-2},\mathrm{-8})$

$(0,7)$ and $(4,\mathrm{-9})$

$(\mathrm{-43},17)$ and $(23,\mathrm{-34})$

What are the coordinates of the origin?

If a point is located on the y -axis, what is the x -coordinate?

If a point is located on the x -axis, what is the y -coordinate?

$\left(4,1\right)\left(\mathrm{-2},\mathrm{-3}\right)\left(5,0\right)$

$(\mathrm{-1},2)(0,4)(2,1)$

$\left(\mathrm{-3},0\right)\left(\mathrm{-3},4\right)\left(\mathrm{-3},\mathrm{-3}\right)$

Name the coordinates of the points graphed.

Name the quadrant in which the following points would be located. If the point is on an axis, name the axis.

$\begin{array}{l}a.\left(\mathrm{-3},\mathrm{-4}\right)\\ b.\left(\mathrm{-5},0\right)\\ c.\left(1,\mathrm{-4}\right)\\ d.\left(\mathrm{-2},7\right)\\ e.\left(0,\mathrm{-3}\right)\end{array}$

$y=\frac{1}{3}x+2$

$y=\mathrm{-3}x+1$

$2y=x+3$

$4x-3y=12$

$x-2y=8$

$y-5=5x$

$3y=\mathrm{-2}x+6$

$y=\frac{x-3}{2}$

Find the distance between the two endpoints using the distance formula. Round to three decimal places.

Find the coordinates of the midpoint of the line segment connecting the two points.

Find the distance that $\left(\mathrm{-3},4\right)$ is from the origin.

Find the distance that $\left(5,2\right)$ is from the origin. Round to three decimal places.

Which point is closer to the origin?

${\text{Y}}_1=\mathrm{-2}x+5$

${\text{Y}}_1=\frac{3x-8}{4}$

${\text{Y}}_1=\frac{x+5}{2}$

${\text{Y}}_1=\mathrm{-8}x+6$

${\text{Y}}_1=4x-7$

${\text{Y}}_1=\frac{3x+5}{4}$ Round your answer to the nearest thousandth.

A man drove 10 mi directly east from his home, made a left turn at an intersection, and then traveled 5 mi north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?

If the road was made in the previous exercise, how much shorter would the man’s one-way trip be every day?

Given these four points: $A\left(1,3\right),B\left(-3,5\right),C\left(4,7\right),\text{ and }D\left(5,\mathrm{-4}\right),$ find the coordinates of the midpoint of line segments $\overline{\text{AB}}$ and $\overline{\text{CD}}.$

After finding the two midpoints in the previous exercise, find the distance between the two midpoints to the nearest thousandth.

Given the graph of the rectangle shown and the coordinates of its vertices, prove that the diagonals of the rectangle are of equal length.

In the previous exercise, find the coordinates of the midpoint for each diagonal.

The coordinates on a map for San Francisco are $\left(53,17\right)$ and those for Sacramento are $\left(123,78\right).$ Note that coordinates represent miles. Find the distance between the cities to the nearest mile.

If San Jose’s coordinates are $\left(76,\mathrm{-12}\right),$ where the coordinates represent miles, find the distance between San Jose and San Francisco to the nearest mile.

A small craft in Lake Ontario sends out a distress signal. The coordinates of the boat in trouble were $\left(49,64\right).$ One rescue boat is at the coordinates $\left(60,82\right)$ and a second Coast Guard craft is at coordinates $\left(58,47\right).$ Assuming both rescue craft travel at the same rate, which one would get to the distressed boat the fastest?

A man on the top of a building wants to have a guy wire extend to a point on the ground 20 ft from the building. To the nearest foot, how long will the wire have to be if the building is 50 ft tall?

If we rent a truck and pay a $75/day fee plus $.20 for every mile we travel, write a linear equation that would express the total cost $y,$ using $x$ to represent the number of miles we travel. Graph this function on your graphing calculator and find the total cost for one day if we travel 70 mi.