Core Mathematics

1The midpoint of (−2, 5) and (6, −1) is

2Find the gradient of the line joining (−2, 3) and (4, −9).

3The vertices of a triangle are (1, 1), (5, 1) and (3, 5). Its area is

4Find the area of the triangle with vertices (0, 0), (4, 0) and (4, 6).

5Find the equation of the line with gradient 2 that passes through (0, −3).

6The line 3x + ky = 6 has gradient −3/2. Find k.

7Find the midpoint of the line joining (2, 4) and (6, 10).

8Find the distance between the points (1, 2) and (4, 6).

9Find the gradient of a line perpendicular to the line joining (1, 2) and (3, 6).

10Find the coordinates of the point dividing (2, 3) and (8, 9) internally in the ratio 1 : 2.