Question

geometry 1.2 distance and midpoint fo name: anbelina kata - b warm up use the figure below for questions 1 - 4. 1. give another name for line r. 2. name the intersection of lines r and s. 3. name three collinear points. 4. give another name for plane n. use the figure below for questions 5. if de = 4x - 1, ef = 9, and df = 9x - 22, find the value of x. 6. if df = 78, de = 5x - 9, and ef = 2x + 10, find ef. definitions main ideas/questions notes distance formula used to find the distance betwee formula:

Explanation:

Step1: Recall line naming

Line $r$ can also be named line $AB$.

Step2: Identify intersection

Intersection of $r$ and $s$ is point $B$.

Step3: Find collinear points

Points $D$, $B$, $C$ are collinear.

Step4: Rename plane

Plane $N$ can be plane $ABCD$.

Step5: Solve for $x$ in question 5

Since $DE + EF=DF$, we have $(4x - 1)+9 = 9x - 22$.
$4x+8 = 9x - 22$, $5x=30$, $x = 6$.

Step6: Solve for $x$ then $EF$ in question 6

Since $DE + EF=DF$, $(5x - 9)+(2x + 10)=78$.
$7x+1 = 78$, $7x=77$, $x = 11$. Then $EF=2x + 10=2\times11 + 10=32$.

Answer:

1. Line $AB$
2. Point $B$
3. $D$, $B$, $C$
4. Plane $ABCD$
5. $x = 6$
6. $EF = 32$