A point P is located at (2, 3) in the 2D plane. The following vector is applied to point P.
$$\begin{bmatrix} 3 \\ -2 \\ \end{bmatrix}$$
What is the new position of point P after the vector translation?
(5, 1)
1 mark for correctly adding the x-coordinates.
1 mark for correctly adding the y-coordinates.
If a point P(2, 5) is translated by the vector v to (5, 3), what is the column vector v?
$$\begin{bmatrix} 3 \\ -2 \\ \end{bmatrix}$$
1 marks for the correct x translation value.
1 mark for the correct y translation value.
In vector notation, the vector A to B is represented as \(\vec{AB} = 3\vec{i} - 2\vec{j}\) and the vector B to C is represented as \(\vec{BC} = -\vec{i} + 4\vec{j}\).
What is the vector C to A?
\(\vec{CA} = -2\vec{i} - 2\vec{j}\)
1 mark for correctly finding the vector B to A.
1 mark for correctly adding the vectors B to A and B to C to find the vector C to A.
Consider a rectangle with vertices at the points (0,0), (0,3), (4,0) and (4,3) on a coordinate plane.
The rectangle undergoes a translatation and the 4 vertices move to (5,2), (5,5), (9,2) and (9,5).
Describe the translation using a column vector.
$$\begin{bmatrix} 5 \\ 2 \\ \end{bmatrix}$$
1 marks for the correct x translation value.
1 mark for the correct y translation value.
A point is located at coordinates (2, 3).
The point undergoes a transformation and moves to (6, 0).
Describe the transformation using a column vector.
Translation and $$\begin{bmatrix} 5 \\ 2 \\ \end{bmatrix}$$
1 mark for identifying translation.
1 mark for the correct column vector.
A rectangle has vertices at points A (2, 1), B (5, 1), C (5, 3) and D (2, 3) on a coordinate plane.
The rectangle is translated according to the vector v:
$$\begin{bmatrix} 4 \\ -2 \\ \end{bmatrix}$$
What are the coordinates of the translated rectangle?
E (6, -1), F (9, -1), G (9, 1) and H (6, 1)
3 marks for all correct.
2 marks for any 3 correct.
1 mark for any 1 correct.
In a coordinate plane, point A is at (2, 3) and point B is at (4, 7).
Translate point A by the vector:
$$\begin{bmatrix} 3 \\ -1 \\ \end{bmatrix}$$
Translate point B by the vector:
$$\begin{bmatrix} -2 \\ 2 \\ \end{bmatrix}$$
What are the new coordinates of points A and B?
Point A is now at (3, 4) and point B is now at (5, 8).
1 mark for correctly translating point A's x-coordinate.
1 mark for correctly translating point A's y-coordinate.
1 mark for correctly translating point B's x-coordinate.
1 mark for correctly translating point B's y-coordinate.
If a point A(1, 4) is translated by the vector v to (4, 2), what is the column vector v?
$$\begin{bmatrix} 3 \\ -2 \\ \end{bmatrix}$$
1 marks for the correct x translation value.
1 mark for the correct y translation value.
Given the vectors of A to B as \(\vec{a}\) and B to C as \(\vec{b}\) , find the vector of C to A?
-a - b
1 mark for understanding that the vector from C to A is the negative of the vector from A to C. 1 mark for correctly applying this to find the vector -a - b.
Given the vectors A to B as \(3\vec{i} + 2\vec{j}\) and B to C as \(2\vec{i} - 4\vec{j}\), calculate the vector C to A.
\(-5\vec{i} + 2\vec{j}\)
1 mark for correctly identifying that both vector A to B and B to C need to be reversed, giving -3i - 2j or -2i + 4j.
1 mark for correctly calculating the resultant vector C to A.
Express the following fraction with a rationalised denominator:
3√2/2
1 mark for multiplying both the numerator and denominator by √2.
1 mark for the correct answer.
Simplify the following surd: √50 + 2√2
7√2
1 mark for simplifying √50 = 5√2
1 mark for combining like terms to reach 7√2
Simplify the following expression by rationalising the denominator:
\( \frac{5}{\sqrt{3} - \sqrt{2}} \)
\( 5\sqrt{3} + 5\sqrt{2} \)
1 mark for multiplying numerator and denominator by the conjugate of the denominator.
1 mark for correctly applying the difference of two squares formula in the denominator.
1 mark for simplifying the expression correctly.
Simplify the following expression by rationalising the denominator:
\( \frac{5}{\sqrt{3} - \sqrt{2}} \)
\( 5(\sqrt{3} + \sqrt{2}) \)
1 mark for multiplying numerator and denominator by the conjugate of the denominator.
1 mark for correctly applying the difference of two squares formula in the denominator.
1 mark for simplifying the expression correctly.
F P2: 
H P2: 
