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.

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A Cartesian coordinate plane with x-axis and y-axis labeled and spanning from -10 to 10 in both directions. Plotted on this grid is a right triangle labeled with vertices P, Q, and R. Point P is located at $\left(-3,-1\right)$(−3,−1), point Q at $\left(-3,-4\right)$(−3,−4), and point R at $\left(2,-4\right)$(2,−4).

Find the length of interval $PQ$PQ.

Find the length of interval $QR$QR.

If the length of $PR$PR 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 $\left(x_1,y_1\right)$(x1,y1)and $\left(x_2,y_2\right)$(x2,y2)?

Medium

< 1min

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

Hard

2min

Outcomes

11.CG.SL.1

Brief recall of 2D from earlier classes. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axes, point-slope form, slope-intercept form, two-point form, intercepts form and normal form. General equation of a line. Distance of a point from a line.

Distances on the Plane (using Pythag)

Interactive practice questions

Outcomes

11.CG.SL.1

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