A Coordinate Plane has both its axes ranging from $0$0 to $40$40, in increments of $2$2. A triangle with vertices labeled $A$A, $B$B, and $C$C, is plotted on the Coordinate Plane. Vertex $A$A is located at $\left(3,7\right)$(3,7). Vertex $B$B is located at $\left(3,4\right)$(3,4). Vertex $C$C is located at $\left(7,4\right)$(7,4). The coordinates of the vertices are not explicitly labeled in the graph.

Complete the steps which calculate the length $AC$AC:

$AC^2=AB^2+BC^2$AC2=AB2+BC2

$AC^2=$AC2=$\left(\editable{}\right)^2+\left(\editable{}\right)^2$()2+()2

$AC^2=$AC2=$\editable{}+\editable{}$+

$AC^2=$AC2=$\editable{}$

Hence find the exact length of $AC$AC.

Easy

1min

Use the triangle and Pythagoras' theorem to complete the following:

Easy

2min

The points $P$P $\left(-6,5\right)$(−6,5), $Q$Q $\left(-6,2\right)$(−6,2) and $R$R $\left(-2,2\right)$(−2,2) are the vertices of a right triangle, as shown on the number plane.

Medium

2min

The points $P$P $\left(-1,9\right)$(−1,9), $Q$Q $\left(-1,6\right)$(−1,6) and $R$R $\left(-5,6\right)$(−5,6) are the vertices of a right triangle, as shown on the number plane.

Medium

1min

Outcomes

MA.912.T.1.2

Solve mathematical and real-world problems involving right triangles using trigonometric ratios and the Pythagorean Theorem.

10.01 Distance and the Pythagorean theorem

Interactive practice questions

Outcomes

MA.912.T.1.2

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