<span>Vector Equation (Line)</span>(x,y) = (x,y) + t(a,b);tERParametric Formx = x + t(a), y = y + t(b); tERr = (-4,-2) + t((-3,5);tERFind the vector equation of the line passing through A(-4,-2) & parallel to m = (-3,5)<span>Point: (2,5) Create a direction vector: AB = (-1 - 2, 4 - 5) = (-3,-1) or (3,1)when -1 (or any scalar multiple) is divided out. r = (2,5) + t(-3,-1);tER</span>Find the vector equation of the line passing through A(2,5) & B(-1,4)<span>x = 4 - 3t y = -2 + 5t ;tER</span>Write the parametric equations of the line passing through the line passing through the point A(4,-2) & with a direction vector of m =(-3,5)<span>Create Vector Equation first: AB = (2,8) Point: (4,-3) r = (4,-3) + (2,8); tER x = 4 + 2t y = -3 + 8t ;tER</span>Write the parametric equations of the line through A(4,-3) & B(6,5)<span>Make parametric equations: x = 5 + 4t y = -2 + 3t ; tER For x sub in -3 -3 = 5 + 4t (-8 - 5)/4 = t -2 = t For y sub in -8 -8 = -2 + 3t (-8 + 2)/3 = t -2 = t Parameter 't' is consistent so pt(-3,-8) is on the line.</span>Given the equation r = (5,-2) + t(4,3);tER, is (-3,-8) on the line?<span>Make parametric equations: x = 5 + 4t y = -2 + 3t ; tER For x sub in 1 -1 = 5 + 4t (-1 - 5)/4 = t -1 = t For y sub in -7 -7 = -2 + 3t (-7 + 2)/3 = t -5/3 = t Parameter 't' is inconsistent so pt(1,-7) is not on the line.</span>Given the equation r = (5,-2) + t(4,3);tER, is (1,-7) on the line?<span>Use parametric equations when generating points: x = 5 + 4t y = -2 + 3t ;tER X-int: sub in y = 0 0 = -2 + 3t solve for t 2/3 = t (this is the parameter that will generate the x-int) Sub t = 2/3 into x = 5 + 4t x = 5 + 4(2/3) x = 5 + (8/3) x = 15/3 + (8/3) x = 23/3 The x-int is (23/3, 0)</span>What is the x-int of the line r = (5,-2) + t(4,3); tER?Note: if they define the same line: 1) Are their direction vectors scalar multiples? 2) Check the point of one equation in the other equation (LS = RS if point is subbed in)What are the two requirements for 2 lines to define the same line?
When any shape is inscribed in a circle, it means that the shape is within the circle but all of the corners are touching the circle. So this could just look like a square within a circle with the corners of the square touching the circle but not going outside of the borders of the circle. Repeat this process with the other shapes. The central angle used to locate the vertices is found by taking the number of sides on the shape and divide it by 360 (the angle of a circle). So for a square with 4 sides, you would take 360/4 and get 90 degrees. This means that each angle within the square is 90 degrees. That 90 degrees is the interior angle of the polygon (for a square specifically). Then what you do is look at the circle and draw a dot at the center of it. You can use a protractor for this part if you want but you would find the central angle by picking a point on the circle and drawing a line to the center dot, then you rotate however many degrees you found in the interior angle of the polygon and you would draw a new line from the center of the circle to that point. You will continue this process until you have gone back to your starting point on the circle. The amount of times it takes you to repeat the process should be the amount of sides the polygon has that you are trying. Interior angle and central angle should be the same for the individual shapes but it would be different for different shapes like a square and an octagon because there are a different amount of sides.
