The line $l_1\,$ passes through the point $A (2, 5)$ and has gradient $−12\displaystyle -\frac{1}{2}$ .

Find an equation of $l_1$ , giving your answer in the form $y = m x + c$ .

The point $B\,$ has coordinates $(- 2, 7)$ . Show that $B\,$ lies on $l_1$ .

Find the length of $A B$ , giving your answer in the form $k5k\sqrt{5}$ , where $k\,$ is an integer.

The point $C\,$ lies on $l_1\,$ and has $x$ -coordinate equal to $p$ . The length of $AC\,$ is 5 units. Show that $p\,$ satisfies

p^2 - 4p - 16 = 0.

The line $l_1\,$ passes through the point $A (2, 5)$ and has gradient $−12\displaystyle -\frac{1}{2}$ .

Find an equation of $l_1$ , giving your answer in the form $y = m x + c$ .

The point $B\,$ has coordinates $(- 2, 7)$ . Show that $B\,$ lies on $l_1$ .

Find the length of $A B$ , giving your answer in the form $k5k\sqrt{5}$ , where $k\,$ is an integer.

The point $C\,$ lies on $l_1\,$ and has $x$ -coordinate equal to $p$ . The length of $AC\,$ is 5 units. Show that $p\,$ satisfies

p^2 - 4p - 16 = 0.

Coordinate Geometry

Coordinate Geometry Questions