Geometry Question???

justinh8

A triangle has vertices, A(1,-1) , B(0,5) and C(-3,0). Find the length of the altitude from A to BC.

You must find the POI of the altitude and BC: thats the hint

So basically i have no idea how to do this....

i got 4.3... but its wrong

symbolipoint

Maybe you would have a better idea of how to continue if you would literally draw the graph. Segment BC forms a line. Can you find the line perpendicular to the line BC which contains the point A? Also what is the equation for the line BC?

SuperNova1

first translate all the points so that one rest on the origin (0,0) this can be easily done.
take A(-1,1) and translate it to (0,0) by adding (1,-1) to it.
this same translation must be used to change ALL the other points so B becomes (0+1,5-1) = (1,4)
then C becomes (-2,-1)
then draw your graph of the triangle with A in the origin
this means you only have two co-ordinates to work from B(1,4) and C(-2,-1)
now with these two points you get the area by using this formula 1/2(xb(yc) - xc(xb))
basically multiply the x coordinate of B (1) by the y coordinate of C (-1) this gives you an answer of -1 then you take away the product of the x coordinate of C (-2) and B(4) which is -8 so you have -1-(-8) so you have 7 divide this by 2 and you have 3.5 units as an area.(remember here that all of these answers are positive as it is area so in another question if you had -7 divided by 2 your area would still be +3.5)
now you can use this equation to find the length of the base (in this example i'll use BC as the base) sqrt((xc-xb)^2 + (yc-yb)^2) so here you have (-2-1)^2 which is (-3)^2 so you have 9 + (-1-4)^2 which ends up as sqrt(9 + 25) = 6 so your length BC is 6.
Now it's simple use your formula half base multiplied by height is area
you have area and you have the base so your unknown is height(altitude)(H)
3.5(area) = 1/2(6) (BASE) * H
3.5= 3*H
H=3.5/3 which is 1.166666666'7 I may have the answer wrong double check it but the method is right (although there are other methods) Try it yourself on paper(computers make maths harder to do) and see what answer you come up with
find area and base then use the formula area=1/2 base*height

phinds

Just FYI, I see that you are new to the forum so perhaps are not aware of it, but it is against policy here to spoon-feed answers. The point of this forum is not to give full worked out answers but to give help that will lead folks to being able to get the answers themselves. In other words, give hints, or a first step. Do NOT give a full worked out answer.

SuperNova1

oh no sorry I didn't realise that will I delete my post?

phinds

I wouldn't bother deleting it. It's done now, and if the OP has email notification turned on, it's already been delivered to him via email.