Question

Answer Questions 9 to 11 using the lines shown in the coordinate grid below.

Question# 5, Is it true that m is parallel to n? Your response should be at least 3 complete sentences. Be sure to include any relevant measurements and angels and calculations for all questions.
Question# 6, Is it true that m is congruent to p?
Question#7 Is it true that n congruent to p?​

Answer 1

5) No the lines are not parallel because in order for this to be true, the slopes have to be equal. Line m has a slope of 2/3 and line n has a slope of 3/5. Both slopes are not equal so it is not parallel

6) No, m is not congruent to p

7) No, n is not congruent to p

(Is there any chance that you meant to say perpendicular instead of "congruent"?)

Explanation:

For two lines to be parallel the slopes have to be equal

See attached to see the rise over run

line m: 2/3

line n: 3/5

The slopes are not equal so the lines are not parallel.

Answer 2

Explanation:

Find the equation of lines m, n and p

The equation of line:

`\boxed {(x-x_1)/(x_2-x_1)=(y-y_1)/(y_2-y_1) }`

Line m: (-3,2) (3,6)

x₁=-3 x₂=3 y₁=2 y₂=6

`\displaystyle\\(x-(-3))/(3-(-3)) =(y-2)/(6-2) \\\\(x+3)/(3+3) =(y-2)/(4) \\\\(x+3)/(6)=(y-2)/(4)`

Multiply both parts of the equation by 4:

`\displaystyle\\(x+3)/(6)(4)=y-2\\\\(2)/(3) (x+3)=y-2\\\\(2)/(3)x+2=y-2\\\\(2)/(3)x+2+2=y-2+2\\\\(2)/(3)x+4=y\\\\Thus,\ y=(2)/(3) x+4\\\\Hence,\ m_m=(2)/(3)`

Line n: (-5,-5) (5,1)

x₁=-5 x₂=5 y₁=-5 y₂=1

`\displaystyle\\(x-(-5))/(5-(-5))=(y-(-5))/(1-(-5)) \\\\(x+5)/(5+5)=(y+5)/(1+5) \\\\(x+6)/(10)=(y+5)/(6)`

Multiply both parts of the equation by 6:

`\displaystyle\\(3)/(5)( x+5)=y+5\\\\(3)/(5) x+3 =y+5\\\\(3)/(5) x+3-5=y+5-5\\\\(3)/(5) x-2=y\\\\Thus,\ y=(3)/(5)x-2\\\\Hence,\ m_n=(3)/(5)`

Line p: (3,-4) (-3,6)

x₁=3 x₂=-3 y₁=-4 y₂=6

`\displaystyle\\(x-3)/(-3-3) =(y-6)/(6-(-4)) \\\\(x-3)/(-6) =(y-6)/(6+4) \\\\(x-3)/(-6)=(y-6)/(10) \\`

Multiply both parts of the equation by 10:

`\displaystyle\\-(5)/(3) x+5=y-6\\\\-(5)/(3) x+5+6=y-6+6\\\\-(5)/(3) x+11=y\\Thus,\ y=-(5)/(3)x+11 \\\\Hence,\ m_p=-(5)/(3)`

`Question# 5: \ m_m\\eq m_n\ \ \ \ m\ isn't\ parallel \ to\ n\\\\Question# 6:\ m\ isn't \ congruent \ to\ p\\\\Question#7 :\ n\ isn't \ congruent \ to\ p`

`n \bot p`