A(2, -4), B(3, 3) C(-1, 5) are the vertices of a triangle. Find the equation of the(i) median through A (ii) altitude through B
Answers
Step-by-step explanation:
i) Median through A will pass through the midpoint of B and C.
Midpoint of B and C =((3-1)/2,(5+3)/2) = (1,4)
Eqn of median through A: (y+4)/(x-2) = (4+4)/(1-2)
(y+4)/(x-2) = -8
y+4 = -8(x-2)
y+4 = -8x+16
y+8x=12
Formula used -> 2 point line equation : (y-y1)/(x-x1) = (y2-y1)/(x2-x1)
Midpoint of 2 points : ((x1+x2)/2,(y1+y2)/2)
ii) Altitude through B will be perpendicular to A and C.
Slope of line between A and C : (5+4)/(-1-2) = -3
Thus, slope of line perpendicular to the line through A and C = -1/-3 = 1/3
Equation of Altitude through B: (y-3)/(x-3) = 1/3
3(y-3) = x-3
3y-9 = x-3
x-3y+6 = 0
Formulas used -> slope point line equation : (y-y1)/(x-x1) = m, where m is the slope of the line.
m1*m2 = -1, m1 being slope of a line, m2 being slope of the line perpendicular to m1
Slope calculation between 2 points: (y2-y1)/(x2-x1)