All of my resources are saying that this has no inverse.
9000 Step by Step Explanation
I just used a calaculator
The rule that describes this transformation is (x - 3, y + 1)
Step-by-step explanation:
Step 1:
The points of the trapezoid are
M; (-3, -1),
N; (-4, 3),
P; (1, 3), and
Q; (-1, -1).
Step 2:
To translate the points to 3 units on the left, we subtract the x coordinate by 3 because it is moved to the left. So x becomes x - 3.
In order to translate the points to 1 unit up, we add 1 to the y coordinate as it is moved in the positive direction of y. So y becomes y + 1.
Combining these we get (x, y) becomes (x - 3, y + 1).
Answer:
Half.
Step-by-step explanation:
It's being divided by two, unlike the second part of the equation. :)
You know that three points A,B,CA,B,C (two vectors A⃗ BA→B, A⃗ CA→C) form a plane. If you want to show the fourth one DD is on the same plane, you have to show that it forms, with any of the other point already belonging to the plane, a vector belonging to the plane (for instance A⃗ DA→D).
Since the cross product of two vectors is normal to the plane formed by the two vectors (A⃗ B×A⃗ CA→B×A→C is normal to the plane ABCABC), you just have to prove your last vector A⃗ DA→D is normal to this cross product, hence the triple product that should be equal to 00:
A⃗ D⋅(A⃗ B×AC)=0