Cartesian Isometric

Age 7 to 11

Challenge Level Yellow star

The graph below is a coordinate system based on

$60$

$^\circ$ angles. It was drawn on isometric paper.

The marked points are

$(6, 2)$ ,

$(6, 5)$ and

$(9, 2)$ . When joined they form an equilateral triangle.

The following five sets of points are also triangles.

A.

$(1, 13), (6, 8)$ and

$(6, 13)$ .
B.

$(1, 1), (3, 3)$ and

$(7, 1)$ .
C.

$(12, 1), (17, 1)$ and

$(8, 9)$ .
D.

$(1, 10), (5, 2)$ and

$(6, 6)$ .
E.

$(7, 5), (15, 4)$ and

$(7, 11)$ .

What kinds of triangles are they?
Can you work out any of the angles at the vertices?

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