Question

Consider three noncollinear points, j, k, and l on a coordinate grid. The y-coordinates of j and k are the same. The x-coordinates of k and l are the same. Is ajkl acute, right, or obtuse? How could you prove it?

Answer 1

The quadrilateral AJKL is a rectangle with all right angles.

Step-by-step explanation:

To determine if the quadrilateral AJKL is acute, right, or obtuse, we need to consider the angles formed by its sides.

• Since the y-coordinates of J and K are the same, the line segment JK is parallel to the x-axis, making angle JKL a right angle.
• Since the x-coordinates of K and L are the same, the line segment KL is parallel to the y-axis, making angle KLJ a right angle.

Based on these properties, angle AJK is a right angle because it is formed by two perpendicular lines. Therefore, the quadrilateral AJKL is a rectangle, which means all of its angles are right angles.