Question

Can anyone HELP with my HOMEWORK for GRADE‼️

Answer 1

Answer:

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

Step-by-step 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,

$hypotenuse^2=leg^2+leg^2$

$hypotenuse^2=2leg^2$

$hypotenuse=leg\sqrt{2}$

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

$AB=AC$

Length of AB is

$AB=\sqrt{(a-0)^2+(0-0)^2}=a$

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.

$AC=\sqrt{(x-0)^2+(0-0)^2}$

$a=x$

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