Question

the base qr of an equilateral triangle pqr with side 10cm lies along x axis such that midpoint of the base is the origin . then the coordinates of the base qr are​

Answer 1

Answer:

Step-by-step explanation:

Let, O be the origin

Since O(0,0) is the mid-point of the base QR

then, QO = OR ( Which means that the points are at an equal distance from the origin O)

Now given that, the length of QR is 10 cm

and the O is the mid-point of the base QR

So, QO = OR = QR/2 = 10/2

or, QO = OR = 5

let, the point Q is at a distance of 5 units to the left of the origin(on the negative side of the x-axis)

⇒ the point R is at a distance of 5 units to the right of the origin(on the positive side of the x-axis)

Therefore, the point Q is (-5,0) and the point R is (5,0)

(NOTE: y-coordinates of the points will be zero as the value of y-coordinate on the x-axis is always zero)

EXTRA: -

Since triangle PQR is an equilateral triangle

so, triangle POQ is a right-angled triangle

using Pythagoras theorem,

(PQ)² = (PO)²+(OQ)²

or, (PO)² = (10)² - (5)²

or, PO = $\sqrt{100-25}$

or, PO = $\sqrt{75}$ = $\sqrt{25\cdot 3}$

or, PO = $5\cdot \sqrt{3}$  ( NOTE: Here PO is the distance between O and P so it cannot be negative )

So, the possible coordinates of P are (-$5\cdot \sqrt{3}$,0) or, (

Answer 2

Given : the base qr of an equilateral triangle pqr with side 10 cm lies along x axis such that midpoint of the base is the origin .  

To Find : Coordinate of q and r

Solution:

qr  lies on x axis

Hence q and  r  coordinates will be of form ( x , 0)

mid point is at origin  Hence

Coordinates of q and r  will be

( h, 0)  and ( -h , 0)  

Distance = |2h |

| 2h | = 10

=> h =  ± 5

Hence coordinates of q and  r will be (  5, 0)  and ( - 5 , 0)

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