Question

this question has two parts. first, answer part a. then, answer part b. part a identify the figure with the vertices a(3,5), b(3,1), and c(0,1). select choice rectangle triangle perimeter: units area: units² need help with this question? get a hint

Explanation:

Step1: Analyze the coordinates

The x - coordinate of points A(3,5) and B(3,1) is the same (x = 3), so the line segment AB is vertical. The length of AB is \(|5 - 1|=4\). The y - coordinate of points B(3,1) and C(0,1) is the same (y = 1), so the line segment BC is horizontal. The length of BC is \(|3 - 0| = 3\). Since there are three vertices and two of the sides are perpendicular (one vertical and one horizontal), the figure is a triangle.

Step2: Calculate the length of the third - side

Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) for points A(3,5) and C(0,1), we have \(AC=\sqrt{(3 - 0)^2+(5 - 1)^2}=\sqrt{9 + 16}=\sqrt{25}=5\).

Step3: Calculate the perimeter

The perimeter \(P\) of a triangle with side lengths \(a\), \(b\), and \(c\) is \(P=a + b + c\). Here, \(a = 3\), \(b = 4\), \(c = 5\), so \(P=3 + 4+5 = 12\).

Step4: Calculate the area

The area \(A\) of a right - triangle with base \(b\) and height \(h\) is \(A=\frac{1}{2}bh\). Here, the base \(b = 3\) and height \(h = 4\), so \(A=\frac{1}{2}\times3\times4 = 6\).

Answer:

Part A: triangle
perimeter: 12 units
area: 6 units²