Coordinate Geometry

Original post by Cool-Light

Question:

The points A(-1, -2), B(7, 2) and C(k, 4), where k is a constant, are the vertices of △ABC. Angle ABC is a right angle.

(a) Find the gradient of AB.

(b) Calculate the value of k.

(c) Find an equation of the straight line passing through B and C. Give your answer in the form ax + by + c = 0, where a, b and c are integers.
Gradient of AB = 1/2.

I don't understand how the gradient BC is perpendicular, someone help me understand please?

I am not sure what you are asking

AB and BC are perpendicular because ABC is a right angle

Reply 2

OP

I don't know how to explain it in terms of words.
I searched the definition of perpendicular in the Oxford 'Concise dictionary of Mathematics' and it is defined as, and I quote: 'At right angles to another. Can be of two lines, two planes, a line and plane, or a line and a surface. Now I understand the definition of perpendicular :smile:

and have an idea. This if off the topic - if something isn't perpendicular nor parallel, how would that type of object look like if given coordinates or an image? could someone show me an example please?

Reply 3

Original post by Cool-Light

I don't know how to explain it in terms of words.
I searched the definition of perpendicular in the Oxford 'Concise dictionary of Mathematics' and it is defined as, and I quote: 'At right angles to another. Can be of two lines, two planes, a line and plane, or a line and a surface. Now I understand the definition of perpendicular :smile:

and have an idea. This if off the topic - if something isn't perpendicular nor parallel, how would that type of object look like if given coordinates or an image? could someone show me an example please?

I have no idea what your problem is

Do you now know how to do the question in the OP

Are you asking what lines look like if they are neither parallel nor perpendicular - if so, they cross at an angle

Reply 4

Annie Gull

I know how to solve this question...it's simply easy!

Reply 5

OP

Original post by TenOfThem

I have no idea what your problem is

Do you now know how to do the question in the OP

Are you asking what lines look like if they are neither parallel nor perpendicular - if so, they cross at an angle

what is OP? And thanks for briefly explaining this: if something isn't perpendicular nor parallel, how would that type of object look like if given coordinates or an image? could someone show me an example please?

Reply 6

Original post by Cool-Light

what is OP?

Opening Post

if something isn't perpendicular nor parallel, how would that type of object look like if given coordinates or an image? could someone show me an example please?

Are you really not sure what 2 lines look like if they cross but not at right angles?

Reply 7

ModernScholar

10

I'm not sure I see the point here... :confused:

In all seriousness though, why haven't you simply plotted the co-ordinates and joined the dots? That would tell you what the triangle looks like and would be how to draw it (find graph paper).

(edited 10 years ago)

Reply 8

OP

Original post by TenOfThem

Opening Post

Are you really not sure what 2 lines look like if they cross but not at right angles?

I don't know something like this: / and this \ crossing at the MP?

Reply 9

Original post by Cool-Light

I don't know something like this: / and this \ crossing at the MP?

Well crossing yes

I would like to help you here but I have no idea what your confusion is, sorry

Reply 10

i'm confused here, do you understand what to do in the question or not? if you don't, what don't you understand?

Reply 11

OP

I've done the question now. Sorry I've dragged it this long, I was just confused to why I couldn't use Point A (-1,-2) to work out C (K,4) and still not too sure? I think (because you guys here helped me to an extent, thank you :smile:

) it's because A and C aren't perpendicular that's why we can't use A to work out the value of K? I swear I need to have the lobotomy done, I'm going crazzzzzyyy
The points A(-1, -2), B(7, 2) and C(k, 4), where k is a constant, are the vertices of △ABC

(edited 10 years ago)

Reply 12

yes, ac and bc aren't perpendicular. have you tried drawing the coordinates to help you answer the question?

also, if we know that bc and ab are perpendicular, what does that tell us about their gradients?

Reply 13

OP

Original post by chocolatemonkey7

yes, ac and bc aren't perpendicular. have you tried drawing the coordinates to help you answer the question?

also, if we know that bc and ab are perpendicular, what does that tell us about their gradients?

-1/m? something to do with that I don't knowwww! I just got the gradient = -2
because I did -1/1/2, 2/1 x - 1 = -2?

Reply 14

Yes!! the gradient of BC is -2, what do we do from here??

try to find the gradient of bc with the unknown k and equate that to -2...

(edited 10 years ago)

Reply 15

OP

Original post by chocolatemonkey7

Yes!! the gradient of BC is -2, what do we do from here??

try to find the gradient of bc with the unknown k and equate that to -2...

Bloody hell, 'Yes!!' you win the lottery or something haha :wink:

I've already done the question :P k = 6, therefore y = -2x+16
in the form of ax+by+c = o => 2x+y-16 = 0, ta da. Thanks

Reply 16

OP

how do I do this ?
(3 + 4 sqr root 3) - 3 sqr root 3/ (2+ sqr root 3) - 1

Reply 17

Yep that's the answer. when you get a maths question right, it does feel like you've won the lottery....well done.....

by the way, is this from C1??

Reply 18

first things first, rationalize the fraction that you have. and then tell me what you've got....

Reply 19

OP