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Triangle ABC has vertices A (-5, 4), B (1, -2) and C (3, 6),
That triangle is:
(a)Write the equation of the line of which AB is a segment.
That's the green line below:
(b)Write the equation of the line of which the altitude to line AC is a segment.
That's the blue line below:
Since it is an altitude, it is perpendicular to AC.
First we find the slope of AC:
The blue line is perpendicular to AC so its slope is
the reciprocal of with the opposite sign, so the
blue line's slope is and it passes through B(1,-2)
(c) Write the equation of the perpendicular bisector of line AC.
We find the midpoint of AC, using the midpoint formula:
Midpoint = (,) = (,) = (,) = M(-1,5)
Now we find the equation of the red line through M(-1,5), it has the same
slope as the altitude since both are perpendicular to the line AC.
The red line's slope is also but it passes through M(-1,5)
(d)Find the perimeter of triangle ABC.
We use the distance formula to find the lengths of all three sides.
So the perimeter = AB + BC + AC =