Construction: Draw a line segment from vertex A intersecting BC at the midpoint (D).
(i)Equation of median AD, we will find the midpoint of side BC
Now using two point form of the equation of the line, we have
Equation of side AD:
13x - y - 13 + 4 = 0
13x - y - 9 = 0
So, required equation of altitude is 3x - y - 9 = 0.
(ii) For the equation of altitude, we will need slope as we have a point through which line passes (A).
Now we will find the slope of side BC and using the relation between the slopes of perpendicular lines, i.e. m1 .m2 = - 1 we will find the slopes of altitude.
Using slope intercept form, we will first calculate intercept,
y = mx + c ……………………(1)
Putting in equation (1)
So, required equation of altitude is 3x + 5y - 23 = 0.
(iii)We have a slope of perpendicular and a mid point from the previous solution
Now for perpendicular bisector, it passes through the midpoint of BC, i.e. we have a slope of the equation and a point through which it passes so we can use the slope - intercept form and calculate intercept,
y = mx + c …………………(i)
Putting in equation (i) value of c,
So, the required equation of perpendicular bisector is 3x + y + 11 = 0.
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