Question

MEDALS (geometry)
Determine whether R(3, 2), O(6, 3), and Q(6, 2) can be the vertices of a triangle.

Answer 1

find the distances of the sides

Answer 2

the question what the shortest side to o to line OR if OQ perpendicular to QR

Answer 3

\[d=\sqrt{(y_1-y_2)^2+(x_1-x_2)^2}\]
distance formula.
plug in each two points to find the distance btw them.

Answer 4

Woops, misread it.

Answer 5

what ? so do i not do that ?

Answer 6

?

Answer 7

No, I think I read it write. So you do do the distance formula. Draw the triangle with the sides and label the sides.
(For your first step)

Answer 8

a.
no:
QR + RO = QO
distance ≈ 1
b.
no:
QR + QO = RO
distance ≈ 4
c.
yes:
QR + RO < QO
QR + QO < RO
QO + RO < QR
distance ≈ 4
d.
yes:
QR + RO > QO
QR + QO > RO
QO + RO > QR
distance ≈ 1
these are the answers

Answer 9

just to show you what i need to find

Answer 10

Don't do ≈, give me the exact value, like sqrt of.
also did you mean vertex (instead of vertices)

Answer 11

im confused, i dont know how to wok out the problem i know how to do the distance thing but that dosent give me my answer

Answer 12

Yeah, and I am kind of a bad helper too (and bad mathmatician). But, anyway...

We have a triangle.
O-R=(3,1) and Q-R=(3,0). These are linearly independent.
So clearly it is a triangle, not just a line.
OQ=Q-O=(0,-1) and from before QR=-RQ=(-3,0).
We see that these sides are perpendicular as 'OQ,QR' =-3*0-1*0=0
and because OQ is perpendicular to QR, it is the shortest line from O to QR. Therefore the shortest distance is the length of OQ which is 1.