Step-by-step explanation:
a) The gradient of AB
The gradient is the ratio of the change in y values to the change of the x values (that is, (1-3)/(7-1))
therefore the gradient =-2/6
b) The gradient of the line perpendicular to AB
It's the negative reciprocal of the gradient of AB (That's gradient (perp.)=-1/gradient (AB))
=-1/(-2/6)
gradient=3
c) Equation of the perpendicular line through (4,2)
The formula for finding an equation of a line is
y-the y coordinate of a point in a line = gradient ( x-the x coordinate of a point in a line)
y-2=3(x-4)
y-3x+4-2=0
y-3x+2=0 is the line
