GeometryWatch

Thread starter 12 years ago
#1
Points A,B,C and D have co-ordinates (1,1), (1,-2), (-2,-3, and (0,5) respectively. They form a quadrilateral. I need to find the lengths of the diagonals (which I assume means lines A->C and B->D) and the angle between the diagonals. I assume the length of the diagonals can be found using pythagoras (I got sqrt(17) and 5), but I don't understand what it means by the angles between them. All help appreciated.
0
reply
12 years ago
#2
(Original post by DoMakeSayThink)
Points A,B,C and D have co-ordinates (1,1), (1,-2), (-2,-3, and (0,5) respectively. They form a quadrilateral. I need to find the lengths of the diagonals (which I assume means lines A->C and B->D) and the angle between the diagonals. I assume the length of the diagonals can be found using pythagoras (I got sqrt(17) and 5), but I don't understand what it means by the angles between them. All help appreciated.
If you draw them on a diagram, the diagonals form a cross; the question is asking for the angle formed by their intersection at the centre of this cross. (There will be two pairs of equal angles at this point; if you find one, you've got all 4.)
0
reply
12 years ago
#3
If i were you I'd set it up using the scalar product.
0
reply
12 years ago
#4
For a start, I get 5 and root(50) for the lengths. Then it's hinting to use the scalar product. Vectors CA = (3,4) and BD = (-1,7).
dotting gives 25 = 5root(50)cos(t). or cos(t) = 1/root(2). t = 45 degrees. That's the angle nearest (0,5) and (1,1). You can work the rest out.
0
reply
Thread starter 12 years ago
#5
Thanks for the help. I had sqrt(17) for one of the sides, not the diagonal, I just didn't make my diagram clear enough... doh!
0
reply
12 years ago
#6
Could you just use

Distance = √(x2-x1)2-(y2-y1)2
0
reply
12 years ago
#7
doesn;t give the angle though
0
reply
X

Write a reply...
Reply
new posts
Latest
My Feed

Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

University open days

• University of the West of England, Bristol
Undergraduate Open Afternoon - Frenchay Campus Undergraduate
Wed, 23 Jan '19
• University of East London
Postgraduate Open Evening Postgraduate
Wed, 23 Jan '19
• University of Gloucestershire
School of Education Open Day Postgraduate
Wed, 23 Jan '19

Poll

Join the discussion

Remain (1623)
79.13%
Leave (428)
20.87%

View All
Latest
My Feed

Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.