Linear Equations II

Hong Kong

Stage 1 - Stage 3

The points $P$`P` $\left(-3,-1\right)$(−3,−1), $Q$`Q` $\left(-3,-4\right)$(−3,−4) and $R$`R` $\left(2,-4\right)$(2,−4) are the vertices of a right-angled triangle, as shown on the number plane.

a

Find the length of interval $PQ$`P``Q`.

b

Find the length of interval $QR$`Q``R`.

c

If the length of $PR$`P``R` is denoted by $c$`c`, use Pythagoras’ theorem to find the value of $c$`c` to three decimal places.

Easy

3min

How far is the given point $P$`P`$\left(-5,-12\right)$(−5,−12) from the origin?

Medium

1min

Which of the following is the formula for finding the distance between two points $\left(x_1,y_1\right)$(`x`1,`y`1)and $\left(x_2,y_2\right)$(`x`2,`y`2)?

Medium

< 1min

Use Pythagoras’ theorem to find the exact length of interval $AB$`A``B`, drawn on the number plane below.

Hard

2min

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