(6) B to c Y2=4 X2=4 ACLI), B(4,2), C(1,4) (a) A to B x=1 9,=1 x1 =4 , 9,=1 42=2 X2=1 X(t) = 1+ (4-)t (t) = 4+ (1-4) Z polt)=4-3t xlt)=1+3t y(t) = 1+(2-1) t lylt=1+32 y(t)=1tt (6) A toc x=1 9,=1 x2= 14=4 X(t)=1+(1-12 X(t)=1 y(t) = 1+(4-1) ly(t) = 1 +32 9 (t)= 1 +(4-1)
The parametric equations below describe the line segment that joins the points P1(X1,Y1) and P2(x2,12). Consider...
The parametric equations where 0 tl describe the line segment that joins the points P1(x1, y and P2(x2, y2) Use a graphing device to draw the triangle with vertices A(1, 1), B(3, 4), C(1,7). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma- separated list of equations. Let x and y be in terms of t.) A to B B to C A to C The parametric equations where 0 tl describe the line...
1 The parametric equations x = x2 + (x2 - *,), y = y + (72 - Y2) where osts i describe the line segment that joins the points P2(XqrY,) and P2(%20Yz). Use a graphing device to draw the triangle with vertices A(1, 1), B(5, 4), C(1,6). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma-separated list of equations. Let x and y be in terms of t.) A to B B to C...
Given distinct points P1= (x1,y1) and P2= (x2, y2),suppose P=(x,y) is any point on a line through P1 andP2. a. By equating slopes, show that x and y satisfy the equation b. Explain why the equation found in (a) is the equation of a straight line. c. What happens if x2 = x1? **PLEASE SHOW ALL WORK!!
Find parametric equations for the line described below. 30) The line through the points P(-1, -1, -1) and Q(7,-5,7) Find a parametrization for the line segment beginning at P1 and er 31) P1(3, 0, -2) and P2(0, 5, 0)
(a) If C is the line segment connecting the point (X1,Y1) to the point (X2, y2), find the following. Jexdy-y x dy - y dx O A = (b) If the vertices of a polygon, in counterclockwise order, are (X1,Y1), (x2, y2), ..., (Xn, Yn), find the area of the polygon. O A = 3 [(x112 - – *287) + (x3X3 – x3y2) + ... + (*n – 1'n – XnYn – 1) + (xn/1 – xqYn] = {[(x112 +...
(a) If C is the line segment connecting the point (X1,Y1) to the point (X2, y2), find the following. e x dyr dy - y dx xly2 - x2y1 x A= A= (b) If the vertices of a polygon, in counterclockwise order, are (X1,Y1). (X2, y2), ..., (X, Yn), find the area of the polygon. [0x271 – 1/2) + (x392 – x2Y3) + .. + ... + (xnxn-1 - xn-1n) + (*11n – Xnxx)] + x2+1) + (x2y + x372)...
Find parametric equations for the segment joining the given points. (1, 3) and (3,6) c(t) = { 1 +31, 2+36 ), ostsi
Find a vector equation and parametric equations for the line segment that joins P to Q. (D |-1+2-) 1 P(0, -1, 4) 4 -t.2 3 t. r(t) 4 vector equation X 7 4 t.2 3 1 - t. (x(t), y(t), z(t)) 4 X - parametric equations 2 If two objects travel through space along two different curves, it's often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) The curves might...
(a) Give a set of parametric equations (with domain) for the line segment from (4, -1) to (5,6). (b) Give a set of parametric equations (with domain) for the ellipse centered at (0,0) passing through the points (4,0), (-4,0), (0,3), and (0, -3), traversed once counter-clockwise. (c) Find the (x, y) coordinates of the points where the curve, defined parametrically by I= 2 cost y = sin 2t 0<t<T, has a horizontal tangent.
2) Find a rectangular equation for the curve with the given parametric equations. x = 2 sin(t).y = 2 cos(t);0 st <270 (b) x2 + y2 = 2 c) x2 + y2 = 4 (d) y = x2 - 4 (a) y2 - x2 = 2 (e) y = x2 - 2