Question

Can anyone HELP with my HOMEWORK for GRADE‼️

Answer 1

The coordinates of point C are (a,0).

Explanation:

Given information: ABC is right isosceles triangle.

From the given figure it is noticed that the side BC is hypotenuse of the triangle ABC.

By pythagoras theorem,

`hypotenuse^2=leg^2+leg^2`

`hypotenuse^2=2leg^2`

`hypotenuse=leg√(2)`

Therefore hypotenuse cannot be equal to leg. So, we can say that in triangle ABC,

`AB=AC`

Length of AB is

`AB=√((a-0)^2+(0-0)^2)=a`

From the figure it is noticed that the point C lies on the x-axis, therefore the y-coordinates of C is 0.

Let the coordinates of C be (x,0) and length of AC must be a.

`AC=√((x-0)^2+(0-0)^2)`

`a=x`

Therefore coordinates of point C are (a,0).