Question

A)
Use the distance formula to calculate which set of coordinate points make a rectangle.
(1 point)
A (1, 2) , B(1, 10) ; C (6, 10) , D(6, 2)
A (4, 2) , B(1, 10) ; C (6, 10) , D(6, 4)
A (6, 4) , B(4, 6) ; C (6, 10) , D(4, 10)
A (2, 2) , B(1, 10) ; C (2, 10) , D(6, 2)
A)
Point
lies at
and point
lies at
. Which point is needed so that
isscalene?
(1 point)
A (−4, 4) B (−3, 6) △ABC
C (−2, 4)
C (−3, 2)
C (−1, 4)
C (−5, 6)

Answer 1

1) The rectangle is A (1, 2), B (1, 10), C (6, 10), D (6, 2).
- AB = sqrt((1−1)^2 + (10−2)^2) = 8
- BC = sqrt((6−1)^2 + (10−10)^2) = 5
- CD = 8, DA = 5 and the diagonals are equal, so the shape is a rectangle.

2) For A(−4,4) and B(−3,6), choose C(−1,4) to make △ABC scalene.
- AB = sqrt(1^2 + 2^2) = sqrt5
- AC (to (−1,4)) = sqrt(3^2 + 0^2) = 3
- BC (to (−1,4)) = sqrt(2^2 + (−2)^2) = sqrt8
All three side lengths are different, so the triangle is scalene.