35 verify the parallelogram abcd with vertices a(-5, -1), b(-9, 6), c(-1, 5), and d(3, -2) is a rhombus by showing that it is a parallelogram with perpendicular diagonals.

- Equal midpoints of AC and BC.

- The product of the slopes of the diagonals AC and DB is -1.

Step-by-step explanation:

1. Plot the given points, as you can see in the graph attached.

2. Calculate the midpoint of AC and DB:

Therefore, the midpoint of AC and DB are equal.

3. Calculte the slope of the diagonals AC and DB:

4. Multiply the slopes of the diagonals:

(AC and DB are perpendicular)