Question

show that a triangle with vertices at the points $(-1,-5),(0,2)$, and $(3,-2)$ is a right triangle.
(type an integer or a simplified fraction.)
find the slope of the segment through $(-1,-5)$ and $(0,2)$.
the slope of the segment through $(-1,-5)$ and $(0,2)$ is 7.
(type an integer or a simplified fraction.)
find the slope of the segment through $(3,-2)$, and $(0,2)$.
the slope of the segment through $(3,-2)$, and $(0,2)$ is $-\frac{4}{3}$.
(type an integer or a simplified fraction.)
find the slope of the segment through $(-1,-5)$ and $(3,-2)$.
the slope of the segment through $(-1,-5)$ and $(3,-2)$ is $\frac{3}{4}$.
(type an integer or a simplified fraction.)
find the product of the slopes of the two segments meeting at the point $(-1,-5)$.
the product of the slopes of the two segments meeting at the point $(-1,-5)$ is $square$.
(type an integer or a simplified fraction)

Explanation:

Step1: Identify the slopes

The slope of the segment through \((-1, -5)\) and \((0, 2)\) is \(m_1 = 7\). The slope of the segment through \((-1, -5)\) and \((3, -2)\) is \(m_2=\frac{3}{4}\).

Step2: Calculate the product of slopes

We need to find the product of the slopes of the two segments meeting at the point \((-1, -5)\). The formula for the product of two numbers \(a\) and \(b\) is \(a\times b\). Here, \(a = 7\) and \(b=\frac{3}{4}\). So the product is \(7\times\frac{3}{4}=\frac{21}{4}\).

Answer:

\(\frac{21}{4}\)