Question

lets try: find the perimeter of δabc. round to the nearest tenth if necessary. a(-3, 5), b(4, 5), c(1, -4)

Explanation:

Step1: Find length of AB

Since A(-3, 5) and B(4, 5) have the same y - coordinate, the distance \( AB=\vert4 - (-3)\vert=\vert4 + 3\vert = 7\)

Step2: Find length of AC

Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), for A(-3, 5) and C(1, - 4), \(x_1=-3,y_1 = 5,x_2=1,y_2=-4\)
\(AC=\sqrt{(1-(-3))^2+(-4 - 5)^2}=\sqrt{(4)^2+(-9)^2}=\sqrt{16 + 81}=\sqrt{97}\approx9.8\)

Step3: Find length of BC

Using the distance formula, for B(4, 5) and C(1, - 4), \(x_1 = 4,y_1=5,x_2=1,y_2=-4\)
\(BC=\sqrt{(1 - 4)^2+(-4 - 5)^2}=\sqrt{(-3)^2+(-9)^2}=\sqrt{9 + 81}=\sqrt{90}\approx9.5\)

Step4: Find the perimeter

Perimeter \(P=AB + AC+BC=7+\sqrt{97}+\sqrt{90}\approx7 + 9.8+9.5 = 26.3\)

Answer:

26.3