Question

1-Findes the length indicated.2- Find the angle indicated.3-Find the distance between each pair of points.

Answer 1

1.

LM = LN - MN

LM = 22 - 5 (Replacing)

LM= 17 (Subtracting)

2.

m∠EDW= m∠EDC - m∠WDC

m∠EDW= 106° - 40° (Replacing)

m∠EDW= 66° (Subtracting)

3.

Using the formula for the distance between two points we have:

`\begin{gathered} d=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ x1=8,x2=-6,y1=3,y2=3 \\ d=\sqrt[]{(8-(-6))^2+(3-3)^2}\text{ (Replacing)} \\ d=\sqrt[]{(8+6)^2+(0)^2}\text{ (Subtracting)} \\ d=\sqrt[]{(14)^2^{}}\text{ (Adding)} \\ d=14\text{ (Raising 14 to the power of 2 and taking the square root)} \\ d=14 \\ \text{ The distance between these points is 14} \end{gathered}`

Using the formula for the midpoint we have:

`\begin{gathered} ((x1+x2)/(2),(y1+y2)/(2)) \\ x1=8,x2=-6,y1=3,y2=3 \\ ((8+(-6))/(2),(3+3)/(2)) \\ ((2)/(2),(6)/(2))\text{ (Subtracting and adding)} \\ (1,\text{ 3) (Dividing)} \\ \text{The midpoint is (1,3)} \end{gathered}`