Find a value of y such that the triangle with the given vertices has an area of 26 square units.
(-6,-6),(2,-2),(-9,y)

A)y = -1 or y = -14
B)y = -1 or y = 14
C)y = -1 or y = 0
D)y = 1 or y = 14
E)y = 1 or y = -14

Question

​Find a value of y such that the triangle with the given vertices has an area of 26 square units. ​
​(-6,-6),​(2,-2),​(-9,y)
​
A)​y = -1 or y = -14
B)​y = -1 or y = 14
C)​y = -1 or y = 0
D)​y = 1 or y = 14
E)​y = 1 or y = -14

Quizplus · Accepted Answer

The area of a triangle given three vertices $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ can be calculated using the formula: $\frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$. Substituting the given points (-6,-6), (2,-2), and (-9,y) into this formula and setting it equal to 26 (since we want the area to be 26 square units), we can solve for $y$. After simplifying the equation, we find that $y$ must satisfy the equation leading to the solutions $y = -1$ or $y = -14$, which matches option A.

​Find a Value of Y Such That the Triangle with the Given

Find a Value of Y Such That the Triangle with the Given