Question

this question has two parts. first, answer part a. then, answer part b. part a identify the figure with the vertices g(-4,1), h(4,1) and i(0,-2) select choice selected choice triangle quadrilateral perimeter units area units² need help with this question? get a hint

Explanation:

Step1: Identify the figure type

Since there are 3 vertices $G(-4,1)$, $H(4,1)$ and $I(0, - 2)$, it is a triangle.

Step2: Calculate the lengths of the sides using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

For side $GH$: $x_1=-4,y_1 = 1,x_2=4,y_2 = 1$. Then $d_{GH}=\sqrt{(4+4)^2+(1 - 1)^2}=\sqrt{8^2+0^2}=8$.
For side $GI$: $x_1=-4,y_1 = 1,x_2=0,y_2=-2$. Then $d_{GI}=\sqrt{(0 + 4)^2+(-2 - 1)^2}=\sqrt{16 + 9}=\sqrt{25}=5$.
For side $HI$: $x_1=4,y_1 = 1,x_2=0,y_2=-2$. Then $d_{HI}=\sqrt{(0 - 4)^2+(-2 - 1)^2}=\sqrt{16+9}=\sqrt{25}=5$.

Step3: Calculate the perimeter

The perimeter $P=d_{GH}+d_{GI}+d_{HI}=8 + 5+5=18$.

Step4: Calculate the area

Since $GI = HI = 5$ and $GH=8$, the base can be $GH = 8$ and the height from $I$ to $GH$ (the vertical distance) is the difference in the $y$ - coordinates of $I$ and the $y$ - coordinate of points on $GH$, which is $1-(-2)=3$. The area formula for a triangle is $A=\frac{1}{2}\times base\times height$. So $A=\frac{1}{2}\times8\times3 = 12$.

Answer:

Part A: triangle
perimeter: 18 units
area: 12 units²