Determine whether a figure with the given vertices is a rectangle using the distance formula.

a(4, –7), b(4, –2), c(0, –2), d(0, –7)

Distance of AB=Distance of CD

and Distance of BC=Distance of DA

Therefore the opposite sides of rectangle ABCD are congruent to each other

Step-by-step explanation:

Let ABCD be the rectangle

and the points A(4,-7), B(4,-2), C(0,-2), D(0,-7)

Now to verify that the given points can figure as a rectangle by using distance formula

Distance of AB

Let be the points A(4,-7), B(4,-2)

Therefore d=5units

Distance of BC

Let be the points  B(4,-2) and C(0,-2)

Therefore d=4units

Distance of CD

Let be the points  C(0,-2) and D(0,-7)

Therefore d=5units

Distance of DA

Let be the points  D(0,-7) and A(4,-7)

Therefore d=4units

Therefore Distance of AB=Distance of CD

and Distance of BC=Distance of DA

Therefore the opposite sides of rectangle ABCD are congruent to each other

{3 + i, 3 - i, 3, -1}

step-by-step explanation: