Question

what is the perimeter of triangle abc? 20 units 22 units 24 units 26 units

Explanation:

Step1: Find coordinates of points

From the graph, we can determine the coordinates:

• Point \( A \): Let's assume the grid has each square as 1 unit. Looking at the x - coordinate, \( A \) is at \( x=-3 \), and y - coordinate \( y = 4 \), so \( A(-3,4) \)
• Point \( B \): \( x = 3 \), \( y=4 \), so \( B(3,4) \)
• Point \( C \): \( x=-3 \), \( y = - 4 \), so \( C(-3,-4) \)

Step2: Calculate length of \( AB \)

The distance formula between two points \( (x_1,y_1) \) and \( (x_2,y_2) \) is \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). For \( A(-3,4) \) and \( B(3,4) \), since \( y_1=y_2 = 4 \), the distance \( AB=\vert x_2 - x_1\vert=\vert3-(-3)\vert=\vert6\vert = 6 \) units.

Step3: Calculate length of \( AC \)

For \( A(-3,4) \) and \( C(-3,-4) \), since \( x_1=x_2=-3 \), the distance \( AC=\vert y_2 - y_1\vert=\vert-4 - 4\vert=\vert-8\vert = 8 \) units.

Step4: Calculate length of \( BC \)

Using the distance formula for \( B(3,4) \) and \( C(-3,-4) \):
\( BC=\sqrt{(3-(-3))^2+(4 - (-4))^2}=\sqrt{(6)^2+(8)^2}=\sqrt{36 + 64}=\sqrt{100}=10 \) units.

Step5: Calculate the perimeter

The perimeter of a triangle \( P=AB + AC+BC \)
Substitute the values: \( P=6 + 8+10=24 \) units.

Answer:

24 units