Triangle ABC has vertices A(0.6), B(4,6), and C(1,3). ketch a graph and use it to find the orthocenter, including any necessary points or slopes you had to deri

Question

Triangle ABC has vertices A(0.6), B(4,6), and C(1,3). ketch a graph and use it to find the orthocenter, including any necessary points or slopes you had to derive.
Given Triangle ABC with A(-4,-2), B(4,4), and C(18,-8), answer the question 21-23.
Write the equation of the line containing the altitude that passes through B in standard form.
Write the equation of the line containing the median that passes through point c in slope-intercept form.
Write the equation for the line containing perpendicular bisector of line AC in point-slope form.

 

I solved problem one and came up with the answer (1,5).

Can someone help me understand how to solve the other three problems. 

Answer 1

I did the first one to see if you were correct.  When I drew my triangle on the coordinate system, and drew the three altitudes, the three lines intersect at (1, 5).   That point is the orthocenter.  You are correct here.  Good work.

 

For the last problems, you will need to draw the triangle with the new points on a coordinate system.  After that, here is what you need to do.

 

In the first of the last questions, you need to draw the triangle.  Then draw the altitude that passes through point B. Use the altitude that passes through point B.  That altitude is your line.  Use the endpoints of that line to find the slope.  Once you have the slope, use the point-slope form of the equation of a line:

y - y₁ = m(x - x₁)

 

where:

m = slope

(x₁ , y₁) is any of the two endpoints of that line

 

One you have your line, put it in standard form:

 

Ax + By = C

 

 

In the second of the last questions, you will draw the median that passes through vertex C.  The median is the line that is connected from point C to the midpoint of the side length opposite to vertex C.   Use the endpoints of the median to find the slope.  Once you have the slope, plug that into the point-slope form of the equation.  Once you have your equation, put in this form:

 

y = mx + b

 

 

In the last question,  plot a point at the midpoint of line AC.  Then from there, you will draw a perpendicular line to connect it to another point on the triangle.  We do this so that the line has two points.  Once you have your two points, you know what to do.  Find the slope and use the point-slope form of a line.