Question

what is the area of a triangle with vertices at (0, 0), (4, 0), and (4, 3) on the coordinate plane?
○ 12 square units
○ 5 square units
○ 7 square units
○ 6 square units

question 12 5 pts
a square is plotted with its vertices at (1, 1), (1, 5), (5, 1), and (5, 5). what is the perimeter of the square?
○ 20 units
○ 16 units
○ 8 units

Explanation:

First Question (Triangle Area)

Step1: Identify base and height

The vertices are \((0,0)\), \((4,0)\), and \((4,3)\). The base is the distance between \((0,0)\) and \((4,0)\), so base \(b = 4 - 0 = 4\). The height is the distance between \((4,0)\) and \((4,3)\), so height \(h = 3 - 0 = 3\).

Step2: Use triangle area formula

The formula for the area of a triangle is \(A=\frac{1}{2}\times b\times h\). Substitute \(b = 4\) and \(h = 3\): \(A=\frac{1}{2}\times4\times3\).

Step3: Calculate the area

\(\frac{1}{2}\times4\times3 = 2\times3 = 6\).

Step1: Find the side length

The vertices of the square are \((1,1)\), \((1,5)\), \((5,1)\), \((5,5)\). The side length is the distance between \((1,1)\) and \((1,5)\) (or other adjacent vertices). Using the distance formula for vertical points (\(x\)-coordinates same), side length \(s = 5 - 1 = 4\).

Step2: Use square perimeter formula

The perimeter of a square is \(P = 4\times s\). Substitute \(s = 4\): \(P = 4\times4\).

Step3: Calculate the perimeter

\(4\times4 = 16\).

Answer:

6 square units

Second Question (Square Perimeter)