Question

1.2 distance and midpoint formula
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

1. if de = 4x - 1, ef = 9, and df = 9x - 22, find the value of x.
2. if df = 78, de = 5x - 9, and ef = 2x + 10, find ef.

definitions
main ideas/questions notes
distance formula used to find the distance between two points (x1, y1) and (x2, y2)
formula:

Explanation:

Step1: Recall line naming

A line can be named by any two points on it. So line $r$ can be named line $AB$.

Step2: Identify intersection point

The intersection of lines $r$ and $s$ is point $B$.

Step3: Find collinear points

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

Step4: Rename plane

Plane $N$ can be named plane $ABCD$.

Step5: Solve for $x$ in first - length problem

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

Step6: Solve for $x$ and then $EF$ in second - length problem

Since $DE + EF=DF$, we have $(5x - 9)+(2x + 10)=78$.
$7x+1 = 78$.
$7x = 77$, so $x = 11$. 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. $EF = 32$