define the following term: intersecting lines - concept for euclid’s geometry
define the following term: intersecting lines
intersecting lines – two lines are intersecting if they have a common point. the common point is called point of intersection.
check out the intersect function.
here is one approach:
% generate a rectangular boundry
rectx = [0.1 0.1 0.9 0.9];
recty = [0.1 0.5 0.5 0.1];
rect = polyshape(rectx,recty);

% initialize a figure for display purposes
figure(1);clf
titles = [...
 "all lines";...
 "partially within";...
 "exclusively within"];
for i = 1:3
 subplot(1,3,i)
 hold on
 title(titles(i))
 plot(rect)
 xlim([0 1])
 ylim([0 1])
end

% define the number of line segments to generate
nlines = 25;

% initialize a structure to store the lines (if you need the data later)
lines = struct();

% generate each line, calculate it's intersection conditions, and plot
for i=1:nlines
 
 % generate points for a random line segment
 lines(i).points = rand(2);
 
 % section the line into parts at intersection with the rectangle
 [in, out] = intersect(rect, lines(i).points);
 
 % plot all the lines that were generated
 subplot(1,3,1)
 line(lines(i).points(:,1),lines(i).points(:,2))
 
 % plot lines that are partially within the boundary
 if isempty(in)==0
 subplot(1,3,2)
 line(lines(i).points(:,1),lines(i).points(:,2))
 end
 
 % plot lines that are exclusively within the boundary
 if isempty(out)==1
 subplot(1,3,3)
 line(lines(i).points(:,1),lines(i).points(:,2))
 end
end
here is the output: you can find the radius in the following way. 
write the equation of the line that is perpendicular to the given tangent line. this perpendicular goes through the stated center, and intersects the tangent; the perpendicular's slope is the negative reciprocal of the stated tangent line.
find the intersection (point t) of the tangent and radius line--then use the distance formula to find the radius, which is a segment from the stated center to the point t. the graph of this equation is a line.  we know that because each term is either a constant (1.5) or the product of a constant and the first power of a variable (d, 0.8t).
since we have two variables (d and t), the line sits in a two-dimensional plane, with a vertical axis and a horizontal axis.  d stands alone in the equation, so its value depends on the value oft.  therefore, the vertical--or dependent--axis will represent values of d, and the horizontal--or independent--axis will represent values of t.
at this point, then, we can set up a coordinate plane with a vertical axis labeled d and a horizontal axis labeled t.  all of the points on our plane have a coordinate (t, d).
to graph a line, we need two points.  since the question asks for the axial intercepts anyway, we can use those.
we'll start with the d-intercept, where the line crosses the d-axis.  all of the points on the d-axis have a t-coordinate of zero, so to find where the line crosses the axis, we substitute zero for t in our equation and solve.
d = 1.5 + 0.8 × t
d = 1.5 + 0.8 × (0)
d = 1.5 + 0
d = 1.5
so our d-intercept has the coordinates (0, 1.5), and we have our first point and our first intercept.
similarly, to find the t-intercept, we note that all of the points on the t-axis have a d-coordinate of zero, so we set d equal to zero and solve.
d = 1.5 + 0.8 × t
0 = 1.5 + 0.8 × t
0 - 1.5 = 1.5 - 1.5 + 0.8 × t
-1.5 = 0.8 × t
-1.5 ÷ 0.8 = (0.8 ÷ 0.8) × t
-1.875 = 1 × t
-1.875 = t
and the d-intercept is (-1.875, 0).
now we have both axial intercepts, so that part of the question is complete.  we can plot those two points and draw the line that passing through them (extending on, at either side, to infinity).
all that remains is to find the turning points.  a turning point, also called a local maximum or local minimum, is where the value of a function goes from decreasing to increasing or from increasing to decreasing.  (the graph shown at http://en.wikipedia.org/wiki/file:parabola\_with\_focus\_and\_directrix.svg has a minimum at the origin, for example.)
a line has a constant slope.  to say that differently, the angle between any two points on a line is the same as the angle between any two other points on the line.  if a line is increasing in one location (like our line), it is increasing everywhere, and it is increasing everywhere at the same rate.  therefore, a line has no turning points. coefficient of friction is defined as the ratio of the force of friction acting between two objects and the force which is pushing them together. the value of the coefficient of friction varies from zero to one. there are two types of the coefficient of friction: static coefficient of friction kinetic (also known as sliding) coefficient of friction. therefore, the coefficient of friction depends on the nature of the surface. answer: 15
solution: there are six straight lines `l\_(1),l\_(2),l\_(3),l\_(4),l\_(5),l\_(6)` in a plane.   
 since no two lines are parallel and no three of which pass through the same point, we have maximum points of intersection.   
 line `l\_(1)` intersect five lines, so there will be five points of intersection.   
 similarly, for each of the lines `l\_(2),l\_(3),l\_(4),l\_(5),l\_(6)`, there will be five points of intersection.   
 but there will be double counting .   
 so, total number of points of intersection is `(5xx6)/(2)=15` we first define our axisupward is along + y direction of axiseastward is along + x direction of axisvelocity of a aeroplane = velocity of a bullet = a person on the earth will see the bullet having a resultant velocity and angle θ with the vertical (y axis)θ = angle with the vertical (y axis) May as well promote my comment to an answer.


You need to add points to a `Curve2D` object, then adjust the control points of the curve, and then finally draw the curve. So here's some simple, almost pseudo code:



```
var array_of_line_points # This already has the vectors which describe our line
for point in array_of_line_points:
  # The "get_perpendicular_vector()" function returns a vector that's a copy of the point, yet has been slid along a line parallel to two neighboring points. The "distance" variable is how far the control point should be from the originating point.
  var control_point1 = get_perpendicular_vector(point, distance)
  var control_point2 = get_perpendicular_vector(point, -distance)
  curve.add_point(point, control_point1, control_point2)
# ...In the draw function
func _draw():
  draw_polyline(curve.get_baked_points(), red, 2.0)

```

I got the inspiration for this from [Rob Spencer's page on Spline Interpolation](http://scaledinnovation.com/analytics/splines/aboutSplines.html). I'd like to make this more thorough (i.e. defining the `get_perpendicular_vector()` function). But this is the best I can currently do. technical vocab – phil 1010 lecture 2 key: terms – \_\_\_ topics – \_\_\_ important – \_\_\_  what is an argument? o arguments are statements that represent an inference. o premises are statements that support a conclusion.  what is an inference? o inferences are thoughts that we believe is true.  inferences can take place conscious or unconsciously. o inferences are implicit while arguments are explicit. o implicit thoughts are implied, suggested, or understood but not directly expressed. o explicit thoughts are usually overly expressed.  sentences & statements o sentences are grammatically correct string of words. o declarative sentences can be either true or fa 1. to connect ideas
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4. to keep the reader interested and to make the ideas clear
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