Question

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

Explanation:

Step1: Find the length of AB

Points A(-3, 5) and B(4, 5) have the same y - coordinate, so the length of AB is the absolute difference of the x - coordinates.
Length of AB = $|4 - (-3)| = |4 + 3| = 7$

Step2: Find the height from C to AB

The line AB is horizontal (since y - coordinates of A and B are equal) with y = 5. The height from point C(1, - 4) to the line AB is the vertical distance between y = 5 and y=-4.
Height h = $|5 - (-4)| = |5 + 4| = 9$

Step3: Calculate the area of the triangle

The formula for the area of a triangle is $A=\frac{1}{2}\times base\times height$. Here, base = AB = 7 and height = 9.
So, $A=\frac{1}{2}\times7\times9=\frac{63}{2}=31.5$

Answer:

31.5