# The Base Qr of a N Equilateral Triangle Pqr Lies on X-axis. the Coordinates of the Point Q Are (-4, 0) and Origin is the Midpoint of the Base. Find the Coordinates of the Points P and R. - Mathematics

The base QR of a n equilateral triangle PQR lies on x-axis. The coordinates of the point Q are (-4, 0) and origin is the midpoint of the base. Find the coordinates of the points P and R.

#### Solution

Let(x ,0) be the coordinates of R. Then

0= (-4+x)/2 ⇒ x =4

Thus, the coordinates of R are (4,0)  . Here, PQ = QR =  PR  and the coordinates of P lies on . y  - axis Let the coordinates of P be

(0,y) . Then ,

PQ = QR ⇒ PQ^2 = QR^2

⇒ (0+4)^2 +(y-0)^2 = 8^2

⇒ y^2 = 64-16=48

⇒ y = +- 4 sqrt(3)

"Hence, the required coordinates are " R (4,0) and P (0,4 sqrt(3) ) or P (0, -4 sqrt(3) ).

Concept: Coordinate Geometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 30