Trying to help my daughter pass an exam tomorrow.

[Jazsdad]

I haven't done this in 30 years.

3.
Decide whether the lines with the given equatins are perpendicular, parallel, or neither.

A)
y=4x-3
y=2x-3

B)
y=5x+7
y=5x-7

C)
y=2x-3
y=1/2x+2

D)
y=-2x+4
y=-1/2x+4

4.
Line j is perpendicular to the line with the given equation and line j passes through P. write an equation fo line j. (no diagragm is provided)
y=1/3x+5, P(6,2)

19.
Complete the proof by supplying the reasons.
Given:
O is the midpoint of MQ
O is the midpoint of NP
Prove Triangle MON is similar to Triangle QOP (diagram description.. draw an X and lay it on its side line MOQ intersects line NOP. The alternate interior angles are approximately 30 degrees. This is not information that is given. I just eyeballed it.

Statements Reasons

1. O is the midpoint of MQ Given
2. MO =QO Given
3. O is the midpoint of NP Given
4. NO = PO Given
5. angle MON = angle QOP ?
6. Triangle MON = Triangle QOP ?

 

[Guest]

Heaps for 1 posting, here are some guidelines to use....

parallel equations have the same gradient (m) when the equations are in the form of y=mx+c

perpendicular equations have gradients that multiply to give -1


y=1/3x+5, P(6,2)
you are looking at a line perpendicular to this equation ie the gradients multipy to give -1

m1 = (1/3)

m1 . m2 = -1
(1/3) .m2 = -1
m2 = -3

the second equation has a gradient of -3 and passes through the point P(6,2).
Place this information into y=mx +c and solve for "c"
You then have the equation.

Start with these.

 

[pka]

If lines have the same slope then they are parallel.

If two lines have slopes the when multiplied together give −1, they are perpendicular.

Otherwise, neither.

 

[Jazsdad]

Thanks a lot

You all are a god send for me. I remember doing this but I don't know how I got through it

Thanks again

 

[Guest]

further update for your last question re triangle MON = QOP

Statements Reasons

1. O is the midpoint of MQ Given
2. MO =QO Given
3. O is the midpoint of NP Given
4. NO = PO Given
5. angle MON = angle QOP ? ...this is true as they are opposite angles
6. Triangle MON = Triangle QOP ? ....true as you have SSA common

SSA means if 2 sides and an angle are common then the triangles are the same.