Question

isosceles triangle klm is shown below. give the coordinates of l.

Explanation:

Step1: Analyze the isosceles triangle

In an isosceles triangle \( KLM \), \( KM = KL \) (marked with equal segments). Point \( M \) is at \( (0,0) \), and since \( L \) is on the \( x \)-axis (vertical line through \( M \) is \( y \)-axis, so \( L \) has the same \( y \)-coordinate as \( M \)? Wait, no, \( M \) is at \( (0,0) \), and \( L \) is on the \( x \)-axis? Wait, the \( x \)-axis and \( y \)-axis: \( M \) is at \( (0,0) \), and \( L \) should be such that \( ML \) is vertical? Wait, no, looking at the graph, \( M \) is at \( (0,0) \), and \( L \) is on the \( x \)-axis? Wait, the coordinates of \( M \) are \( (0,0) \), and since \( KLM \) is isosceles with \( KM = KL \), the base \( ML \) is horizontal? Wait, no, the \( y \)-axis is vertical, \( x \)-axis is horizontal. So \( M \) is at \( (0,0) \), and \( L \) should be at \( (a,0) \) such that the midpoint of \( ML \) is the projection of \( K \) onto the \( x \)-axis. Wait, but in the graph, \( M \) is at \( (0,0) \), and \( L \) is at \( (2,0) \)? Wait, maybe the length of \( ML \) is such that the \( x \)-coordinate of \( L \) is \( 2 \) (since the problem might have \( M(0,0) \) and \( L(2,0) \), and \( K \) is at \( (1,u) \) because it's isosceles, so the midpoint of \( ML \) is at \( (1,0) \), so \( K \) has \( x \)-coordinate \( 1 \). But the question is about \( L \)'s coordinates. Wait, maybe \( M \) is at \( (0,0) \), and \( L \) is at \( (2,0) \), so the coordinates of \( L \) are \( (2,0) \).

Step2: Confirm the coordinates

Since \( M \) is at \( (0,0) \) and the triangle is isosceles with \( KM = KL \), the base \( ML \) is horizontal (along the \( x \)-axis), so the \( y \)-coordinate of \( L \) is \( 0 \), and the \( x \)-coordinate is \( 2 \) (assuming the length from \( M(0,0) \) to \( L \) is \( 2 \) units, so \( L \) is at \( (2,0) \).

Answer:

The coordinates of \( L \) are \((2, 0)\)