McGraw Hill Glencoe Geometry, 2012
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McGraw Hill Glencoe Geometry, 2012 View details
2. Medians and Altitudes of Triangles
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Exercise 53 Page 343

Calculate the slopes of the lines using the Slope Formula.

Are the Lines Parallel, Perpendicular, or Neither? Neither
Graph:

Practice makes perfect

In order to determine the relationship between the lines, let's calculate each of their slopes.

Slope of RS

We are given the points R(5,- 4) and S(10,0), which lie on RS. Let's substitute them into the Slope Formula and calculate the slope.

m_1=y_2-y_1/x_2-x_1
m_1=0-( - 4)/10- 5
m_1=0+4/10-5
m_1=4/5

Slope of JK

Similarly, by substituting the points J(9,- 8) and K(5,- 13) into the Slope Formula, we can calculate the slope of JK.

m_2=y_2-y_1/x_2-x_1
m_2=- 13-( - 8)/5- 9
m_2=- 13+8/5-9
m_2=- 5/- 4
m_2=5/4

Analyze the Slopes

Now that we know the slopes of the lines, we can determine whether they are parallel, perpendicular, or neither. Remember that parallel slopes are the same and perpendicular slopes are opposite reciprocals. m_1=4/5 m_2=5/4 From here, we can conclude that the lines are neither perpendicular nor parallel.

Graph

Let's graph the lines to verify that they are neither perpendicular nor parallel. We do can this by plotting the points and drawing lines through them.

As we can see, the lines are neither perpendicular nor parallel.