Question

ABC is an isosceles triangle with vertices A(2,0), B(2,5)and C(x,y). find C(x,y) when AC and BC are equal sides of length 3 cm.

Answer 1

Given:-

△ABC is an Isosceles triangle.

B(2,5), A(2,0), C(x, y)

AC = BC = 3cm

To find:-

coordinates of point C(x, y) = ?

Solution:-

As triangle is Isosceles.

•°• AC = BC

• By distance formula

√((x - 2)² + (y - 0)²) = √((x - 2)² + (y - 5)²)

(x - 2)² + (y - 0)² = (x - 2)² + (y - 5)²

(y - 0)² = y² - 10y + 25

y² = y² - 10y + 25

0 = -10y + 25

10y = 25

y = 25/10 = 5/2

y = 5/2 ........(1)

Now, By distance formula

AB = 3cm

•°• 3 = √((x - 2)² + (y - 0)²)

9 = (x - 2)² + (5/2)²

9 = (x - 2)² + 25/4

9 - 25/4 = (x - 2)²

(36 - 25)/4 = (x - 2)²

11/4 = (x - 2)²

x - 2 = √(11/4)

x - 2 = √11/2

x = √11/2 + 2

x = (√11 + 4)/2

• Answer

C(x, y) = ((√11 + 4)/2, 5/2) = (3.65, 2.5)