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O-Level E-Maths Coordinate Geometry and Vectors quiz (SEAB 4052) quiz

13questions. Pick an answer and you'll see why right away.

  1. Find the distance between the points (2,3)(2, 3) and (5,7)(5, 7).

  2. Find the midpoint of (1,4)(1, 4) and (7,10)(7, 10).

  3. Find the gradient of the line through (2,1)(2, 1) and (6,9)(6, 9).

  4. What is the gradient of a line parallel to y=4xβˆ’1y = 4x - 1?

  5. What is the gradient of a line perpendicular to one with gradient 23\dfrac{2}{3}?

  6. Find the equation of the line with gradient 33 passing through (0,βˆ’2)(0, -2).

  7. Find the equation of the line through (1,5)(1, 5) and (3,11)(3, 11).

  8. Given a=(32)\mathbf{a} = \begin{pmatrix} 3 \\ 2 \end{pmatrix} and b=(1βˆ’4)\mathbf{b} = \begin{pmatrix} 1 \\ -4 \end{pmatrix}, find aβˆ’b\mathbf{a} - \mathbf{b}.

  9. Find 3a3\mathbf{a} where a=(2βˆ’1)\mathbf{a} = \begin{pmatrix} 2 \\ -1 \end{pmatrix}.

  10. Find the magnitude of the vector (512)\begin{pmatrix} 5 \\ 12 \end{pmatrix}.

  11. If OA⃗=(12)\vec{OA} = \begin{pmatrix} 1 \\ 2 \end{pmatrix} and OB⃗=(46)\vec{OB} = \begin{pmatrix} 4 \\ 6 \end{pmatrix}, find AB⃗\vec{AB}.

  12. Two vectors are parallel if one is a scalar multiple of the other. Which vector is parallel to (23)\begin{pmatrix} 2 \\ 3 \end{pmatrix}?

  13. What does it mean if ABβƒ—=2 BCβƒ—\vec{AB} = 2\,\vec{BC}?