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, )B (0, 4)C (0, )D (, 0)E (4, )
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it would be on y axis
so x coordinate 0
SO IT'S A,B,C
so x coordinate 0
SO IT'S A,B,C
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1
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).
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