Question

isosceles triangle cde is shown below. give the coordinates of e.
c(0, s)
d(-r, 0) e(?, ?)
e ( , )

Explanation:

Step1: Analyze the isosceles triangle

In isosceles triangle \( CDE \), \( CD = CE \) (marked by the tick marks), and the base \( DE \) is on the x - axis. The vertex \( C \) is on the y - axis at \( (0,s) \). The point \( D \) is at \( (-r,0) \). Since the triangle is isosceles with respect to the y - axis (the axis of symmetry), the x - coordinate of \( E \) should be the mirror image of the x - coordinate of \( D \) with respect to the y - axis. The y - coordinate of \( E \) is the same as the y - coordinate of \( D \) because both \( D \) and \( E \) lie on the x - axis (where \( y = 0 \)).

Step2: Find the x - coordinate of \( E \)

The x - coordinate of \( D \) is \( -r \). The reflection of a point \( (x,y) \) over the y - axis is \( (-x,y) \). So, reflecting \( D(-r,0) \) over the y - axis, the x - coordinate becomes \( r \) and the y - coordinate remains \( 0 \).

Answer:

\( (r,0) \)