Question

Given triangle ABC with A(-3,2), B(-1,4) and C(4,1) write the equation for the line containing altitude segment AR in standard form.
a. x-y=1
b. x+y=-1
c. x+y=1
c. x-y=-1

Answer 1

2. Given triangle ABC with A(-3,4), B(5,8), and C(2,-2) write the equation of the line containing midsegment XZ in standard form, where X is the midpoint of segment AB and Z is the midpoint of segment BC.
a. 6x-5y=-24
b. 2x+5y=32
c. 2x-5y=-28
d. 6x+5y=36

Answer 2

it looks unfamiliar at all, do you have any idea to solve it? for the first one first, don't make a lot like this, it's easy confused.

Answer 3

Um All I know is that the altitude is the perpendicular bisector connecting to the vertex of the oppisite side.

Answer 4

do we have a pic?

Answer 5

no... this is exactly how the question is formated

Answer 6

can we draw a pic by ourselves ?

Answer 7

Yeah hang on and I'll draw it

Answer 8

thank you, I really want to know what happen

Answer 9

oops, I have an idea, it may help. Think of this: we find the slope of the line BC, so, the slope of the line AR will be -1/ slope of BC.
Then, we have slope, and a point A, we can write out the line \(\bot\)BC at A
do you think it works?

Answer 10

I'm kind of confused. I know the slope of AR would be -1. so now I need to find the equation for AR in standard form which I don't know how to do that.

Answer 11

no,no, the slope of AR = \(\dfrac {-1}{slope~~of~~BC}\) , we have to find slope of BC, how can you know it's =-1? We didn't have any proof of this, don't you think we should have a logic to back up our argument?

Answer 12

I used an online slope calculator to save time because I really need to get this done like now and it said the slope of BC is 1 and the slope of a perpendicular line is the negative recipricol so therefor it would be -1

Answer 13

@Opcode @rose21 @douglaswinslowcooper can any of you guys help?

Answer 14

my guess for 1 is b because it would contain point (-3,2) and my guess for 2. is d am I right?

Answer 15

@hartnn can you help really quick? Its almost midnight and I've been working on this all day.

Answer 16

You have your slope from knowing it had to be the negative of the reciprocal of the slope of the base.

Now use the slope of your new line in the equation
y = (slope) x + b,
plugging in the x,y coordinates of the point you have to go through, the apex of the triangle. Home free after that!