MATH SOLVE

3 months ago

Q:
# The coordinates of the vertices of △JKL are J(0, 2) , K(3, 1) , and L(1, −5) .Drag and drop the choices into each box to correctly complete the sentences.The slope of JK¯¯¯¯¯ is , the slope of KL¯¯¯¯¯ is , and the slope of JL¯¯¯¯¯ is . △JKL a right triangle because .

Accepted Solution

A:

Answer:Part 1) The slope of JK is [tex]m_J_K=-\frac{1}{3}[/tex]
Part 2) The slope of KL is [tex]m_K_L=3[/tex]
Part 3) The slope of JL is [tex]m_J_L=-7[/tex]
Part 4) Triangle JKL is a right triangle because two of these slopes have a product of -1Step-by-step explanation:we know thatIf two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have[tex]J(0, 2), K(3, 1),L(1, -5)[/tex]Part 1) Find the slope JKwe have[tex]J(0, 2), K(3, 1)[/tex]substitute in the formula[tex]m=\frac{1-2}{3-0}[/tex]
[tex]m_J_K=-\frac{1}{3}[/tex]
Part 2) Find the slope KLwe have[tex]K(3, 1),L(1, -5)[/tex]substitute in the formula[tex]m=\frac{-5-1}{1-3}[/tex]
[tex]m_K_L=\frac{-6}{-2}[/tex]
[tex]m_K_L=3[/tex]
Part 3) Find the slope JLwe have[tex]J(0, 2),L(1, -5)[/tex]substitute in the formula[tex]m=\frac{-5-2}{1-0}[/tex]
[tex]m_J_L=\frac{-7}{1}[/tex]
[tex]m_J_L=-7[/tex]
Part 4) Compare the slopes[tex]m_J_K=-\frac{1}{3}[/tex]
[tex]m_K_L=3[/tex]
[tex]m_J_L=-7[/tex]
we have thatJK and KL are perpendicular because their slopes are opposite reciprocalThe product of their slopes is equal to -1thereforeTriangle JKL is a right triangle because two of these slopes have a product of -1