# Geometrical problems with coordinates

## Interactive practice questions

$A$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.

$ABCD$ABCD is a rhombus as shown on the number plane.

Given Line P: $y=-6x-4$y=6x4, Line Q: $y=\frac{x}{6}+6$y=x6+6, Line R: $y=-6x-1$y=6x1 and Line S: $y=\frac{x}{6}+1$y=x6+1.

### Outcomes

#### 10D.AG2.05

Solve problems involving the slope, length, and midpoint of a line segment

#### 10D.AG3.02

Verify, using algebraic techniques and analytic geometry, some characteristics of geometric figures