Answer: 24.2° SouthWest
<u>Step-by-step explanation:</u>
First step: DRAW A PICTURE of the vectors from head to tail <em>(see image)</em>
I created a perpendicular from the resultant vector to the vertex of the given vectors so I could use Pythagorean Theorem to find the length of the perpendicular. Then I used that value to find the angle of the plane.
<u>Perpendicular (x):</u>
cos 35° = adjacent/hypotenuse
cos 35° = x/160
→ x = 160 cos 35°
<u>Angle (θ):</u>
sin θ = opposite/hypotenuse
sin θ = x/320
sin θ = 160 cos 35°/320
θ = arcsin (160 cos 35°/320)
θ = 24.2°
Direction is down (south) and left (west)
Answer:
Step-by-step explanation:
Given rule for the multiple translations is,

Apply the rule
first.
(x, y) → (-x, -y)
This rule illustrates a rotation of the triangle FGH by 180° about the origin,
Vertices of ΔFGH are,
F → (1, 1)
G → (4, 5)
H → (5, 1)
After rotation vertices of the image triangle are,
F' → (-1, -1)
G' → (-4, -5)
H' → (-5, -1)
Further apply the rule,

(x, y) → (x + 5, y - 0.5)
By this rule of translation,
F'(-1, -1) → F"{(-1 + 5), (-1 - 0.5)}
→ F"(4, -1.5)
G'(-4, -5) → G"[(-4 + 5), (-5 - 0.5)]
→ G"(1, -5.5)
H'(-5, -1) → H"[(-5 + 5), (-1 -0.5)]
→ H"(0, -1.5)
Answer:
2. 2N
3. -4N
4. 4N
5. 7N
Step-by-step explanation: