Question

either prove or disprove the statement, \the points (-5, -3), (-2, -4), and (5,1) are the vertices of a right triangle.\ use a graph only as a guide. by looking at the graph it seems that the points (-5, -3), (-2, -4), and (5,1) do not form a right triangle. note that the right triangle has two sides perpendicular to each other. if (-5, -3), (-2, -4), and (5,1) are the vertices of a right triangle, which of the following must be true?
a. two sides of the triangle must have the sum of their slopes as 0.
b. two sides of the triangle must have the same slope.
c. two sides of the triangle must have the product of their slopes as -1.
d. two sides of the triangle must have the product of their slopes as 1.
what is the formula for the slope of a line through ((x_1,y_1)) and ((x_2,y_2)) with (x_1
eq x_2)?
a. (\frac{y_2 - y_1}{x_2 - x_1})
b. (\frac{y_2 - x_2}{y_1 - x_1})
c. (\frac{x_2 - x_1}{y_2 - y_1})
d. (\frac{y_1 - x_1}{y_2 - x_2})
recall that the three points (-5, -3), (-2, -4), and (5,1) are labeled as a, b, and c respectively. find the slopes of each side of the triangle.
slope (m_{ab}) of the side ab = (square) (type an integer or a simplified fraction.)

Explanation:

Step1: Identify coordinates of A and B

Point A: \((-5, -3)\), Point B: \((-2, -4)\)

Step2: Apply slope formula

Slope formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\)
Substitute \(x_1 = -5\), \(y_1 = -3\), \(x_2 = -2\), \(y_2 = -4\)
\(m_{AB} = \frac{-4 - (-3)}{-2 - (-5)}\)

Step3: Simplify the expression

Simplify numerator: \(-4 + 3 = -1\)
Simplify denominator: \(-2 + 5 = 3\)
So, \(m_{AB} = \frac{-1}{3}\)

Answer:

\(-\frac{1}{3}\)