Question

The coordinates of vertices P and Q of an equilateral triangle PQR are (–4, 0) and (4, 0)respectively. Which of the following could be the coordinates of vertex R?A (0, $\sqrt[2]{3}$)B (0, 4)C (0, $\sqrt[4]{3}$)D ($\sqrt[4]{3}$, 0)E (4, $\sqrt[4]{3}$)

Answer 1

it would be on y axis
so x coordinate 0

SO IT'S A,B,C

Answer 2

Answer:

Concept:

In an equilateral triangle, all three sides are equal.

So, PQ = QR = RP

From the coordinates given of P and Q, we can infer that P and Q lie on the x-axis. The length of the side PQ becomes 8 cm. ( travel from -4 to 4 on the x-axis).

Therefore, PQ = RS = PR = 8 cm.

So, in the triangle, since the point R is located at exactly mid way of PQ, therefore, x - coordinate of R = 0.

Now to find the y - coordinate, use pythgoras theorem.

Side QR = 8cm

and half of base = 4cm

So, let the height of the triangle be x, then

x² + 4² = 8²

or, x² = 64 - 16

or x = √48

or, x = 4√3

or y - axis = 4√3

So, the coordinates of R are (0, 4√3).