1. find the length of $overline{xy}$. explain how you found your answer.
2. a map shows a section of highway 18 that forms a straight line. a family plans to drive 440 miles on highway 18 from springfield to columbia. they drive for 66 miles, and then decide they will stop halfway through their trip to rest for the night. how much farther do they need to drive before they stop for the night?
3. point $m$ is between points $l$ and $n$ on $overline{ln}$. $ln = 6x$, $lm = 4x + 8$, and $mn = 27$. use the information to solve for $x$, and then find $ln$.
use the diagram.
4. give another name for line $s$.
5. name three points that are coplanar.
6. name three points that are collinear.
7. give another name for plane $k$.
8. plot the points in a coordinate plane. then determine whether $overline{ab}$ and $overline{cd}$ are congruent: $a(-2,1), b(2,1), c(3,2), d(3, - 2)$.

Question

Accepted Answer

### 1.
# Explanation:
## Step1: Identify segment parts
The length of $\overline{XY}$ is the sum of the lengths of $\overline{XZ}$ and $\overline{ZY}$.
$XZ = 6$ and $ZY=12$.
## Step2: Calculate length of $\overline{XY}$
$XY=XZ + ZY$.
$XY=6 + 12=18$.
# Answer:
$18$

### 2.
# Explanation:
## Step1: Find halfway - point of trip
The total trip is $440$ miles. The halfway - point is $\frac{440}{2}=220$ miles.
## Step2: Calculate remaining distance
They have already driven $66$ miles. So the remaining distance $d$ is $220−66 = 154$ miles.
# Answer:
$154$ miles

### 3.
# Explanation:
## Step1: Set up equation based on segment addition
Since $L - M - N$, $LN=LM + MN$. Substitute the given expressions: $6x=(4x + 8)+27$.
## Step2: Solve for $x$
First, simplify the right - hand side: $6x=4x+35$. Then subtract $4x$ from both sides: $6x−4x=4x + 35−4x$, which gives $2x=35$, so $x=\frac{35}{2}=17.5$.
## Step3: Find $LN$
Substitute $x = 17.5$ into the expression for $LN$. $LN = 6x=6	imes17.5 = 105$.
# Answer:
$x = 17.5$, $LN = 105$

### 4.
# Explanation:
A line can be named by any two points on the line. Since the line $S$ passes through points $X$ and $U$, another name for line $S$ is line $\overline{XU}$ (or line $\overline{UX}$).
# Answer:
Line $\overline{XU}$

### 5.
# Explanation:
Coplanar points lie on the same plane. Points $T$, $Y$, and $R$ all lie on plane $K$.
# Answer:
$T$, $Y$, $R$

### 6.
# Explanation:
Collinear points lie on the same straight line. Points $X$, $R$, and $U$ lie on the same line (line $S$).
# Answer:
$X$, $R$, $U$

### 7.
# Explanation:
A plane can be named by any three non - collinear points on the plane. Points $T$, $Y$, and $P$ are non - collinear and lie on plane $K$, so another name for plane $K$ is plane $TYP$.
# Answer:
Plane $TYP$

### 8.
# Explanation:
## Step1: Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ for $\overline{AB}$
For $A(-2,1)$ and $B(2,1)$, $x_1=-2,y_1 = 1,x_2=2,y_2 = 1$. Then $d_{AB}=\sqrt{(2-(-2))^2+(1 - 1)^2}=\sqrt{(4)^2+0^2}=4$.
## Step2: Use the distance formula for $\overline{CD}$
For $C(3,2)$ and $D(3,-2)$, $x_1 = 3,y_1=2,x_2=3,y_2=-2$. Then $d_{CD}=\sqrt{(3 - 3)^2+(-2 - 2)^2}=\sqrt{0^2+(-4)^2}=4$.
Since $d_{AB}=d_{CD}=4$, $\overline{AB}$ and $\overline{CD}$ are congruent.
# Answer:
$\overline{AB}$ and $\overline{CD}$ are congruent.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

1.

Step1: Identify segment parts

Step2: Calculate length of $\overline{XY}$

Step1: Find halfway - point of trip

Step2: Calculate remaining distance

Step1: Set up equation based on segment addition

Step2: Solve for $x$

Step3: Find $LN$

Answer:

2.