Concept explainers
(a)
To find: The equation of line k .
(a)
Answer to Problem 5CE
The equation of line k is
Explanation of Solution
Given information: The lines j , k and l contains the altitudes of
Calculation:
Let the line k cut the x- axis at the point P . From the figure it can be observed that the point P has coordinates
It can be seen that the line k is a vertical line or parallel to y -axis. It passes through the points
Therefore, the equation of line k is
(b)
To find: The slope of the line l .
(b)
Answer to Problem 5CE
The slope of the line l is
Explanation of Solution
Given information: The lines j , k and l contains the altitudes of
The slope of the line
Calculation:
It is given that the line l contains the altitude of
The slope of line
The condition for two perpendicular lines is given by,
The slope of the line l can be calculated as:
Therefore, the slope of the line l is
(c)
To show: The equation of the line l is
(c)
Explanation of Solution
Given information: The lines j , k and l contains the altitudes of
Proof:
From part (b), slope of the line l is
The formula to find the equation of a line with given slope that passes through a point is given by,
Substitute 0 for
Hence, it is proved that the equation of the line l is
(d)
To show: The lines k and l intersect at
(d)
Explanation of Solution
Given information: The lines j , k and l contains the altitudes of
Proof:
From part (a), the equation of line k is
To find y -coordinate, substitute b for x in the equation of line l .
Hence, it is proved that the lines k and l intersect at
(e)
To find: The slope of the line
(e)
Answer to Problem 5CE
The slope of the line
Explanation of Solution
Given information: The lines j , k and l contains the altitudes of
Calculation:
The slope of the line
The condition for two perpendicular lines is given by,
From the figure it can be observed that line j is perpendicular to
Therefore, the slope of the line
(f)
To show: The equation of the line j is
(f)
Explanation of Solution
Given information: The lines j , k and l contains the altitudes of
Proof:
From part (e), slope of the line j is
The formula to find the equation of a line with given slope that passes through a point is given by,
Substitute a for
Hence, it is proved that the equation of the line j is
(g)
To show: The lines k and j intersect at
(g)
Explanation of Solution
Given information: The lines j , k and l contains the altitudes of
Proof:
From part (a), the equation of line k is
To find y -coordinate, substitute b for x in the equation of line j .
Hence, it is proved that the lines k and j intersect at
(h)
To write: The coordinates of three altitude lines.
(h)
Explanation of Solution
From part (d) and (g), the lines k , l and j intersect at
Therefore, the coordinates of the point where three altitude lines intersect is
Chapter 13 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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