On a coordinate plane, the vertices of a rectangle are (–1, 1), (3, 1), (–1, –4), and (3, –4). What is the perimeter of the rectangle?

Given that,

The vertices of a rectangle are (–1, 1), (3, 1), (–1, –4), and (3, –4).

To find,

The perimeter of the rectangle.

Solution,

Let the points are :

A(–1, 1), B(3, 1), C(3, –4) and D(–1, –4)

Let's find AB and BC using distance formula :

The perimeter of a rectangle = 2(sum of two adjacent sides)

= 2(AB+BC)

= 2(4+5)

= 18 units

So, the perimeter of the rectangle is 18 units.

b||c; c||d; b||d

Step-by-step explanation:

Substituting 10 for x, in the angle beside b we have

7(10)-5 = 70-5 = 65

In the angle beside c we have

10(10)+15 = 100+15 = 115

In the angle beside d we have

12(10)-5 = 120-5 = 115

In the angle beside we have

8(10)-25 = 80-25 = 55

The angle beside c has a vertical angle on the other side of c.  This angle would be same-side interior angles with the angle beside b; this is because they are inside the block of lines made by b and c and on the same side of a, the transversal.  These two angles are supplementary; this is because 65+115 = 180.  Since these angles are supplementary, this means that b||c.

The angle beside c and the angle beside d would be alternate interior angles; this is because they are inside the block of lines made by c and d and on opposite sides of the transversal.  These two angles are congruent; this means that c||d.

Since b||c and c||d, by the transitive property, b||d.