Distance between two points

Calculate the distance between two points using the distance formula, often involving surds or exact values.

5 questions · Easy -1.2

Sort by: Default | Easiest first | Hardest first

The line $l _ { 1 }$ passes through the point $A ( 2,5 )$ and has gradient $- \frac { 1 } { 2 }$.
1. 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 $k \sqrt { } 5$, where $k$ is an integer. The point $C$ lies on $l _ { 1 }$ and has $x$-coordinate equal to $p$.
The length of $A C$ is 5 units.
Show that $p$ satisfies $$p ^ { 2 } - 4 p - 16 = 0 .$$

Express $\sqrt { 75 } + \sqrt { 48 }$ in the form $a \sqrt { 3 }$.
Express $\frac { 14 } { 3 - \sqrt { 2 } }$ in the form $b + c \sqrt { d }$. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c7fbeb8f-d874-4756-aa53-5471b215902f-3_773_961_354_591} \captionsetup{labelformat=empty} \caption{Fig. 11}
\end{figure} Fig. 11 shows the points A and B , which have coordinates $( - 1,0 )$ and $( 11,4 )$ respectively.