Question

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

Explanation:

Step1: Analyze the isosceles triangle

In isosceles triangle \( KLM \), \( KM = KL \) (marked with equal segments). Point \( M \) is at \( (0,0) \), and we need to find the coordinates of \( L \). Since \( M \) is on the origin and the base \( ML \) is along the x - axis (assuming the vertical axis is y - axis and horizontal is x - axis), and the triangle is isosceles with \( KM = KL \), the x - coordinate of \( L \) should be such that the mid - point of \( ML \) has the same x - coordinate as the x - coordinate of \( K \) (due to the property of isosceles triangles: the altitude from the apex \( K \) to the base \( ML \) bisects the base). Wait, actually, looking at the graph, \( M \) is \( (0,0) \), and if we assume that the base \( ML \) is horizontal, and the triangle is isosceles with \( KM = KL \), then the y - coordinate of \( L \) should be 0 (since \( M \) is at \( (0,0) \) and \( ML \) is a side on the x - axis? Wait, no, the point \( L \) is on the x - axis? Wait, the coordinates of \( M \) are \( (0,0) \), and the triangle is isosceles. Let's assume that the base is \( ML \), and \( K \) is the apex. So the base \( ML \) is horizontal, so both \( M \) and \( L \) have y - coordinate 0. The x - coordinate of \( M \) is 0, and since the triangle is isosceles, the x - coordinate of \( L \) should be such that the mid - point of \( ML \) is directly below \( K \). But from the graph, we can see that the x - coordinate of \( L \) should be \( (2,0) \)? Wait, no, wait the problem says "Give the coordinates of \( L \)". Wait, maybe there is a typo in the original problem's coordinate marking. Wait, looking at the graph, \( M \) is \( (0,0) \), and if we consider that the base \( ML \) is along the x - axis, and the triangle is isosceles, then the coordinates of \( L \) should be \( (2,0) \) (assuming that the distance from \( M(0,0) \) to \( L \) is such that the triangle is isosceles with \( K \) above. Wait, maybe the y - coordinate of \( L \) is 0, and x - coordinate is 2. So \( L=(2,0) \).

Step2: Confirm the coordinates

Since \( M \) is at \( (0,0) \) and the triangle is isosceles, and from the visual representation (the base \( ML \) is along the x - axis), the y - coordinate of \( L \) is 0, and the x - coordinate is 2. So the coordinates of \( L \) are \( (2,0) \).

Answer:

\((2,0)\)