Question

rectangle abcd is graphed in the coordinate plane. the following are the vertices of the rectangle: a(-6, -4), b(-4, -4), c(-4, -2), and d(-6, -2). what is the perimeter of rectangle abcd? units

Explanation:

Step1: Find length of AB

Points A(-6, -4) and B(-4, -4) have same y-coordinate. Length AB = |-4 - (-6)| = |2| = 2.

Step2: Find length of BC

Points B(-4, -4) and C(-4, -2) have same x-coordinate. Length BC = |-2 - (-4)| = |2| = 2? Wait, no, wait: Wait, AB: x from -6 to -4, so distance is 2. BC: y from -4 to -2, distance is 2? Wait, no, wait, rectangle has length and width. Wait, AB: A(-6,-4) to B(-4,-4): difference in x is (-4) - (-6) = 2, so length AB = 2. BC: B(-4,-4) to C(-4,-2): difference in y is (-2) - (-4) = 2? Wait, no, that would make it a square. Wait, no, wait, D is (-6,-2). So AD: A(-6,-4) to D(-6,-2): difference in y is (-2) - (-4) = 2. Wait, so AB is 2, AD is 2? No, that's a square. Wait, perimeter of rectangle is 2(length + width). So length AB: distance between A and B: since y is same, distance is |x2 - x1| = |-4 - (-6)| = 2. Length AD: distance between A and D: x is same, distance is |y2 - y1| = |-2 - (-4)| = 2. Wait, no, that's a square, but square is a rectangle. So perimeter is 2(2 + 2)? No, wait, no, wait, AB is from (-6,-4) to (-4,-4): x changes by 2, so length 2. BC is from (-4,-4) to (-4,-2): y changes by 2, so length 2. Wait, no, that's a square with side 2. Then perimeter is 42 = 8? Wait, no, wait, maybe I made a mistake. Wait, let's recalculate. AB: A(-6,-4), B(-4,-4). The distance between them is sqrt[(-4 - (-6))² + (-4 - (-4))²] = sqrt[(2)² + 0] = 2. BC: B(-4,-4), C(-4,-2). Distance is sqrt[(-4 - (-4))² + (-2 - (-4))²] = sqrt[0 + (2)²] = 2. CD: C(-4,-2), D(-6,-2). Distance is sqrt[(-6 - (-4))² + (-2 - (-2))²] = sqrt[(-2)² + 0] = 2. DA: D(-6,-2), A(-6,-4). Distance is sqrt[(-6 - (-6))² + (-4 - (-2))²] = sqrt[0 + (-2)²] = 2. So it's a square with side 2. Perimeter of rectangle (square) is 2(length + width) = 2(2 + 2) = 8? Wait, no, perimeter of square is 4side, which is 4*2=8. So yes, perimeter is 8.

Answer:

8