Start by drawing a segment from P to any of the vertices. Use this segment to construct a 90^(∘) angle.
Practice makes perfect
We are given a triangle with vertices X, Y, and Z, and a point of rotation P.
We want to draw r_((90^(∘),P))(△ZXY). This means that
we want to rotate △ZXY by 90^(∘) about point P. To do so, we will follow four steps.
Draw PX and construct a 90^(∘) angle with vertex P and side PX.
Construct PX' such that PX' lies on a side of the angle drawn in the previous step and PX'≅ PX.
Locate Y' and Z' in a similar manner.
Connect X', Y', and X' to draw △X'Y'Z'.
Let's do it!
Step 1
Let's draw PX.
We will use a protractor to construct a 90^(∘) angle with vertex P and side PX. We start by placing the center of the protractor on P, making sure that the flat part is on PX.
Notice that the inner measuring scale has 0^(∘) on PX. Therefore, we will use the inner measuring scale. Moreover, recall that if it is not specified, we measure the angle in the counterclockwise direction.
Finally, to construct the angle, we remove the protractor and draw a ray from P that passes through the mark we have just drawn.
Note that for this step, we could have chosen point Y or point Z instead of X. We arbitrarily chose point X for simplicity.
Step 2
We will now locate X', which is the image of X after the rotation. To do so, we will use a compass. We will start by placing the sharp spike of the compass at P, and the leg with the pencil at X.
Without modifying the amplitude of the compass, we will keep the sharp spike at P. Then, we will draw an arc intersecting the ray we drew in the previous step. This point of intersection is X'.
Step 3
We can repeat Step 1 and 2 to find Y'.
Then, we can repeat the same steps to locate Z'.
Step 4
Finally, to draw △X'Y'Z' — which is the image of △ZXY after a rotation of 90^(∘) about P — we will connect the obtained vertices.
