Question

coordinate geometry- I hate it, I don't understand it, but must for a test.... I am confused by it, do not understand the purpose, am confused by the formula, the m and b, and every time I think I have it mastered, I attempt the questions and have them wrong AGAIN!!! Help please.

Answer 1

when I was study, i hate geometry too, but let try to resolve your question)

Answer 2

OK...Thanks. This is the type of question...
When they say

The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC equals 90 degrees, what is the area of triangle ABC?

Answer 3

First, you have probably forgotten how hard it was to learn to read and write, but I would guess you do not think it was useless? Math is also useful, and maybe (other than using it if you want to do science or engineering or financial or management) is that it is a form of thinking, and the only way to get good at thinking is to practice. A new idea is hard to grasp, but once you do learn it, you get better at understanding the next new idea.
And that is the point... otherwise you will be stuck with just the obvious ideas you already know, and be ignorant of good ideas that took people thousands of years to figure out.

Answer 4

angle ABC equals 90 degrees,
that means the line connecting A to B is perpendicular to
line BC
the slope of perpendicular lines are related.
i.e. if the slope of AB is c/d then the slope of the perpendicular line BC is -d/c
(you might see if slope of AB = m then slope of BC = -1/m)

Answer 5

if you are given two points AB, you can find the slope using
change in y divided by change in x

for example, using A(0, 0), B(0, 4a – 5)
the change in y (doing B-A) is
4a-5 - 0= 4a-5
change in x is 0-0 =0
we get m= (4a-5)/0 and that is undefined. i.e. the line is straight up and down
(we could have noticed that the x value is the same for both points, so the two points are one over the other... though until we now what "a" is, we don't know the exact location)

now the slope of B(0, 4a – 5) and C(2a + 1, 2a + 6)
change in y is
2a + 6 - (4a-5) = 2a + 6 -4a + 5
combine 2a-4a (2 a's take away 4 a's, we get -2 a's)
combine 6+5 to get 11
so change in y is -2a+11

change in x is : 2a+1 - 0= 2a+1

slope is (-2a+11)/(2a+1)

this slope is perpendicular to the line AB. line AB goes straight up, so this line
must go horizontal (it this clear ?). Horizontal lines have zero slope
so we know
\[ \frac{-2a+11}{2a+1} = 0 \]
you can multiply both sides by 2a+1 to get
\[ \frac{-2a+11}{\cancel{2a+1}} \cdot \cancel{2a+1}= 0 \cdot (2a+1)\\
-2a+11= 0 \\ 11= 2a \\
a= \frac{11}{2}
\]

Answer 6

now you can figure out the (x,y) values for each of the points.
area of the triangle will be 1/2 * base * height
i.e. the distance up from AB is the height
the width is the distance from B to C, which is the x value of point B