The coordinates of triangle ABC are given as A(2, 5), B(- 4, 5), C(8, - 1). The diagram of the triangle with altitude on each side is shown below
The formula for determining slope is expressed as
Slope = (y2 - y1)/(x2 - x1)
The altitudes are AX, CY and BZ
For line BC,
Slope = (- 1 - - 2)/(8 - 1) = (- 1 + 2)/7
Slope = 1/7
The altitude on BC is AX
Slope of AX = - 1// Slope of BC
Slope of AX = - 1/(1/7) = - 1 * 7/1
Slope of AX = - 7
For line AC,
Slope = (- 1 - 5)/(8 - 2) = - 6/6
Slope = 1
The altitude on AC is BZ
Slope of BZ = - 1/Slope of AC
Slope of BZ = - 1/1
Slope of BZ = - 1
For line AB,
Slope = (1 - 5)/(- 2 - 2) = - 4/- 4 = 1
The altitude on AB is CY
Slope of CY = - 1/Slope of AB
Slope of CY = - 1/1
Slope of CY = - 1
