SOLUTION: The verticies of a triangle are D (6,6) E (-3,0) and F (0,-3). Find the coordinates of the point of intersection of the altitudes of the triangle through D and E. Also prove that t
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-> SOLUTION: The verticies of a triangle are D (6,6) E (-3,0) and F (0,-3). Find the coordinates of the point of intersection of the altitudes of the triangle through D and E. Also prove that t
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Question 797697: The verticies of a triangle are D (6,6) E (-3,0) and F (0,-3). Find the coordinates of the point of intersection of the altitudes of the triangle through D and E. Also prove that the three altitudes are concurrent by showing that this point lies on the the third altitude. Answer by solver91311(24713) (Show Source):
Use the two-point form of an equation of a line to write equations representing the lines containing each of the triangle side segments.
where and are the coordinates of the given points.
Putting each one into slope-intercept form now will simplify the work later.
Step 2:
Using the negative reciprocal of the slope of the line containing points E and F and the point D, as parameters for the point-slope form of an equation of a line, write an equation for the altitude of the triangle through D.
where are the coordinates of the given point and is the calculated slope.
Repeat for the line containing points D and F and the point E.
Step 3:
Solve the 2X2 system of equations consisting of the two equations derived in step 2. This unique ordered pair will be the point of intersection of the altitudes through D and E.
Step 4:
Repeat the process in step 2 for the line containing D and E and point F. Substitute the coordinates of the point of intersection found in Step 3 into this new equation. Verify a true statement.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
