Question

If ( -4,0) and (4,0) are the two vertices of an equilateral triangle, find the coordinates of the third vertex and also find the height of the triangle.

Answer 1

Step-by-step explanation:

Given If ( -4,0) and (4,0) are the two vertices of an equilateral triangle, find the coordinates of the third vertex and also find the height of the triangle.

• So let a triangle ABC having three vertices be drawn. So vertex b has (-4,0) and vertex c will be (4,0)
• So distance BC will be  
•                       √ (4 + 4)^2 + 0^2
•                                 = 8  
• So distance AB will be
•                               √(x + 4)^2 + y^2
• So distance AC will be
•                              √(x – 4)^2 + y^2
• So in equilateral triangle we have
•           AB = AC = BC
• So AB = AC
•     √(x + 4)^2 + y^2 = √(x – 4)^2 + y^2
•       Now we get
•       (x + 4)^2 + y^2 = (x – 4)^2 + y^2
•         x^2 + 8x + 16 = x^2 – 8x + 16
•                          16x = 0
•                               x = 0
•   Now AB = BC
•        √(x + 4)^2 + y^2 = 8
• Squaring on both sides we have
•          (x + 4)^2 + y^2 = 64
•             x^2 + 8x + 16 + y^2 = 64
•                     16 + y^2 = 64 (since x = 0)
•                            y^2 = 64 – 16
•                           y^2 = 48
•                            y = 4√3
• So the coordinates will be A (x,y) = A(0,4√3)

Reference link will be

https://brainly.in/question/3049224#: