The diagram below (see attachment) shows a triangle ABC whose vertices are at A (-1, 3), B (6, 5) and C (8, -3). The line BP is perpendicular to the line AC, and M is the midpoint of BC.

Note that BP is called an altitude of triangle ABC and that AM is called a median of triangle ABC.

a) Find the gradient of
i) The line AC
ii) The altitude BP
(Show answers as a fraction in its simplest form)

b) Find the equation of the altitude BP, expressing your answer in the form: y = mx + c

Answer: slope of line AC= -2/3
ii) The altitude BP

Altitude BP is perpendicular to AC
The product of the gradients of perpendicular lines = -1
Therefore ,
Slope of line AC x slope of line BP = -1
Or ( -2/3) x slope of line BP = -1
Or slope of line BP = -1 / (-2/3) = 3 /2

... Solution: In graphical method of solving system of equations, we graph both the given equations of lines and find out the point of intersection of lines. ...

... graphically: x + y = -1 and y - 2x = -4. Write down the co-ordinates of the point of intersection of the two lines. 3. Solve the system of equations x + 3y ...

... y=3 and purple line shows the graph of line Yx=0 ... graph we can see that the point of intersection is (1 ... solution shows how to solve system of equations by graphing ...

... do these lines intersect? Please see attached file for solution. The solution provides some examples how to solve linear equation and find the intersection. ...

... Using the equation of either line (say the equation of the ﬁrst line), we can ﬁnd the y -coordinate of their point of intersection: 3 3 yD x C 3 D .12/ C 3 ...

... So, for example, some solutions to the first equation (the red line in the ... They could only share one solution, because two lines can only intersect in at ...

... C. What do you notice about the intersection of the two lines? D. Solve the system of equations in part A to determine the degrees of each angle by using ...