Question

1. what is the perimeter of a triangle with vertices a(-2, 7), b(-2, -3), and c(5, 4)? a. 24 units b. 28 units c. 30 units d. 32 units 20. on line segment ac, point b is between a and c. ab = 2x + 1 bc = 3x - 2 ac = 17 find the length of ac. a. 15 b. 17 c. 19 d. 21

Explanation:

Step1: Use segment - addition postulate

Since point B is between A and C, we have $AB + BC=AC$. Given $AB = 2x + 1$, $BC=3x - 2$, and $AC = 17$, we substitute these values into the equation: $(2x + 1)+(3x - 2)=17$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $2x+1 + 3x-2=5x - 1$. So, the equation becomes $5x-1 = 17$.

Step3: Solve for x

Add 1 to both sides of the equation: $5x-1+1=17 + 1$, which gives $5x=18$. Then divide both sides by 5: $x=\frac{18}{5}=3.6$. But we don't need to find x for the length of AC as it is already given.
The length of AC is given as 17.

Answer:

17