Answer:
For question 3, you would just add 2 to the x values and subtract 2 from the y values, so it would be:
J' (-2, 5)
K' (2, 6)
L' (1, 2)
M' (-3, 1)
For question 4 you would subtract 7 from the x values and 6 from the y values, and that would be:
W' (-6, 1)
X' (-1, -1)
Y' (-3, -6)
Z' (-8, -4)
For question 9 you would end up with:
X' (6, -5)
Y' (7, 1)
Z' (4, 0)
For question 10 you would end up with:
Q' (-1, 2)
R' (1, 7)
S' (-2, 6)
T' (-4, 1)
For question 11 you would end up with:
L' (4, 1)
M' (8, 5)
N' (6, 7)
P' (2, 3)
For question 12 you would end up with:
G' (6, -7)
H' (6, -4)
I' (1, -7)
Hope this is what you were looking for!
Step-by-step explanation:
The magic of the internet will help!
Using the dot product:
For any vector x, we have
||x|| = √(x • x)
This means that
||w|| = √(w • w)
… = √((u + z) • (u + z))
… = √((u • u) + (u • z) + (z • u) + (z • z))
… = √(||u||² + 2 (u • z) + ||z||²)
We have
u = ⟨2, 12⟩ ⇒ ||u|| = √(2² + 12²) = 2√37
z = ⟨-7, 5⟩ ⇒ ||z|| = √((-7)² + 5²) = √74
u • z = ⟨2, 12⟩ • ⟨-7, 5⟩ = -14 + 60 = 46
and so
||w|| = √((2√37)² + 2•46 + (√74)²)
… = √(4•37 + 2•46 + 74)
… = √314 ≈ 17.720
Alternatively, without mentioning the dot product,
w = u + z = ⟨2, 12⟩ + ⟨-7, 5⟩ = ⟨-5, 17⟩
and so
||w|| = √((-5)² + 17²) = √314 ≈ 17.720
The messurerments on a ruler and or to determine on a graph
