Answer :

** 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. m_{1} .m_{2} = - 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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