Question

the hypotenuses of 2 triangles, triangle 1 and triangle 2, form a straight line. which statement is correct? the ratio of the horizontal to vertical side of triangle 1 is equal to 1/3 of the ratio of the horizontal to vertical side of triangle 2. the ratio of the hypotenuse to the vertical side of triangle 1 is equal to 1/3 of the ratio of the hypotenuse to the horizontal side of triangle 2. the slope of triangle 1 is 1/1; the slope of triangle 2 is also 1/1. the slope of triangle 1 is -1/1; the slope of triangle 2 is also -1/1.

Explanation:

Step1: Calculate the slope of Triangle 1

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For Triangle 1, if we consider two points \((0,2)\) and \((2,4)\), then \(m_1=\frac{4 - 2}{2-0}=\frac{2}{2} = 1\).

Step2: Calculate the slope of Triangle 2

For Triangle 2, if we consider two points \((- 4,-3)\) and \((-2,-1)\), then \(m_2=\frac{-1+3}{-2 + 4}=\frac{2}{2}=1\).

Answer:

The slope of Triangle 1 is \(1\); the slope of Triangle 2 is also \(1\).