Question

geometry chapter 1 review

1. one step in the construction of \\(\overline{xy}\\), the perpendicular bisector of \\(\overline{ab}\\) is shown.

which of the following is the next step in this construction?
a. label the endpoints of the arc as x and y.
b. using the same compass setting, put the compass point on point b and draw another long arc.
c. put the compass point on point a and draw a long arc as shown. be sure the opening is greater than \\(\frac{1}{2}ab\\).
d. draw \\(\overline{xy}\\), the perpendicular bisector of \\(\overline{ab}\\).

1. which of these is the first step in constructing a congruent segment?

a. draw a ray.
b. draw a line.
c. measure the segment.
d. label two points on the segment.

1. the floor plan of a patio has the coordinates (-2,0), (-2,8), (12,8), and (18,0) when it is placed on the coordinate plane. each unit on the coordinate plane represents 1 foot.

part a: calculate the perimeter and the area of the patio.
perimeter: area:
part b: how many square tiles will it take to cover the floor of the patio if the tiles have a side length of 24 inches?

Explanation:

Step1: Analyze question 18

For constructing the perpendicular - bisector of a line segment $\overline{AB}$, after drawing an arc from point $A$, the next step is to use the same compass setting, put the compass point on point $B$ and draw another long arc.

Step2: Analyze question 19

The first step in constructing a congruent segment is to draw a ray.

Step3: Analyze question 20 Part A

Let the points be $A(-2,0)$, $B(-2,8)$, $C(12,8)$, $D(18,0)$.
The length of $AB$: Using the distance formula for two points with the same $x$ - coordinate, $d=\vert y_2 - y_1\vert$. Here, $AB=\vert8 - 0\vert = 8$ feet.
The length of $BC$: Using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, $x_1=-2,y_1 = 8,x_2=12,y_2 = 8$, so $BC=\vert12-(-2)\vert=14$ feet.
The length of $CD$: Using the distance formula for two points with the same $y$ - coordinate, $d=\vert x_2 - x_1\vert$. Here, $CD=\vert18 - 12\vert = 6$ feet.
The length of $DA$: Using the distance formula, $x_1=-2,y_1 = 0,x_2=18,y_2 = 0$, so $DA=\vert18-(-2)\vert=20$ feet.
The perimeter $P=AB + BC+CD + DA=8 + 14+6 + 20=48$ feet.
The patio is a trapezoid. The area formula for a trapezoid is $A=\frac{(b_1 + b_2)h}{2}$, where $b_1$ and $b_2$ are the lengths of the parallel sides and $h$ is the height. The parallel sides are the horizontal sides with lengths $20$ and $14$, and the height is $8$. So $A=\frac{(20 + 14)\times8}{2}=136$ square feet.

Step4: Analyze question 20 Part B

The side - length of the tile is $24$ inches or $2$ feet. The area of one tile is $A_{tile}=2\times2 = 4$ square feet.
The number of tiles $n=\frac{136}{4}=34$.

Answer:

1. B. Using the same compass setting, put the compass point on point $B$ and draw another long arc.
2. A. Draw a ray.
3. Part A: Perimeter: 48 feet, Area: 136 square feet

Part B: 34