1. Construct a 2x2 matrix

whose elemtns are given by

.

2. In ΔPQR, ST||QR and

.
If PR = 6 cm, find PT.

3. If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.

4. Prove that

.

5. Find the area of the quadrilateral whose vertices are (3,4), (-1,6), (-3,-4), and (6,1).

6. P, Q, R have coordinates (-2,1), (2,2), and (6,-2). Find
(i) the Gradient of the line perpendicular to QR.
(ii) the Gradient of the line parallel to PQ.

7. A (2,-4), B (3,3), and C (-1,5) are the vertices of a triangle ABC. Find the equation of the median of the traingle through A.

8. If m is the slope of a line parallel to 3x + 4y + 7 = 0, find the value of 16m².

9. Show that

if

.

10. If A = 30°, verify

.