7. Find the coordinates of the intersection of the diagonals of the parallelogram with vertices (-2,-4),(-4,4),(2,12) and (4,4) 8. Three vertices of square ABCD are A(1,5),B(1,1) and D(2,2) Find the coordinates of the remaining vertex.

1. Find the fourth vertex of the parallelogram ### Let vertices be A(-2,-4), B(-4,4), C(2,12), D(4,4). Check order: ABCD. ## Step2: Use midpoint formula for diagonals ### Diagonals of a parallelogram bisect each other. Midpoint of AC and BD is intersection point. Use **midpoint formula**: M = \left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right). ## Step3: Calculate midpoint of A(-2,-4) and C(2,12) ### M_1 = \left(\frac{-2+2}{2},\frac{-4+12}{2}\right) = (0,4) ## Step4: Calculate midpoint of B(-4,4) and D(4,4) ### M_2 = \left(\frac{-4+4}{2},\frac{4+4}{2}\right) = (0,4) # Answer: ### (0, 4) --- # Explanation: ## Step1: Assign coordinates to vertices ### A(1,5), B(1,1), D(2,2). Let C(x,y) be the unknown vertex. ## Step2: Use property of rectangle diagonals ### Diagonals bisect each other. Midpoint of AC equals midpoint of BD. ## Step3: Write midpoint equations ### Midpoint of AC: \left(\frac{1+x}{2},\frac{5+y}{2}\right); midpoint of BD: \left(\frac{1+2}{2},\frac{1+2}{2}\right) = (1.5,1.5). ## Step4: Set midpoints equal and solve ### \frac{1+x}{2}=1.5 \implies x=2, \frac{5+y}{2}=1.5 \implies y=-2 # Answer: ### (2, -2)