Linear Equations II

Hong Kong

Stage 1 - Stage 3

$A$`A`$\left(-2,-1\right)$(−2,−1), $B$`B`$\left(0,0\right)$(0,0) and $C$`C`$\left(1,k\right)$(1,`k`) are the vertices of a right-angled triangle with right angle at $B$`B`.

a

Find the value of $k$`k`.

b

Find the area of the triangle.

Easy

Approx 9 minutes

Consider any right-angled triangle with a base of $b$`b` and a height of $h$`h`, placed in the coordinate plane as shown.

$ABCD$`A``B``C``D` is a rhombus as shown on the number plane.

Given Line P: $y=-6x-4$`y`=−6`x`−4, Line Q: $y=\frac{x}{6}+6$`y`=`x`6+6, Line R: $y=-6x-1$`y`=−6`x`−1 and Line S: $y=\frac{x}{6}+1$`y`=`x`6+1.

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