Question

PQR is an equilateral triangle with the coordinates of the Q and R are (0, 4) and (0,-4) respectively. Find the coordinates of the vertex P.

Answer 1

Answer:

coordinate of the vertex p is (6.93,0)

Step-by-step explanation:

From the attached figure, the distance between Q and R is 4 + 4 =8

Hence, QR = 8

Since, it is an equilateral triangle. Hence, all the sides are equal.

Therefore, PQ = PR = QR = 8

Now, vertex p is on the x axis. Hence, the y coordinate is 0.

Let the vertex p is (x,0)

Thus, we have

PQ = 8

⇒$8 = \sqrt{(0-4)^{2} + (x-0)^{2} }$

⇒$16 + x^{2} = 8^{2}$

⇒$x^{2} = 64- 16$

⇒$x^{2} = 48$

⇒$x= \sqrt{48}$

⇒x= 6.93

Thus, coordinate of the vertex p is (6.93,0)

Answer 2

Answer:

(4root3,0)

use a= root3/4 a^2

so a= 16root3

so, 4h=16root3

h=4root3 = vertex p