Has vertices j(3, –1), k(4, –4), and l(1, –3). determine if is an equilateral, isosceles, or scalene triangle. a. equilateral b. isosceles c. scalene d. none of these

To solve this problem we simply need to find the lengths of each side of the triangle. To do this, we use the distance formula: √(x1-x2)^2+(y1-y2)^2. Using points J and K, we find that the length of JK is √(3-4)^2+(-1-(-4))^2=√(-1)^2+(3)^2=√1+9=√10. Then we do the same for JL and KL. JL is √(3-1)^2+(-1-(-3))^2=√(2)^2+(2)^2=√4+4=√8. KL is √(4-1)^2+(-4-(-3)^2)=√(3)^2+(-1)^2=√9+1=√10. Now we have all three sides of the triangle: √10, √8, and √10. Check for any similarities: you have two sides of √10. Because there are two sides of the triangle of the same length, the triangle is an isosceles triangle.