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!!
Given distinct points P1= (x1,y1) and P2= (x2, y2),suppose P=(x,y) is any point on a line...
The parametric equations below describe the line segment that joins the points P1(X1,Y1) and P2(x2,12). Consider the triangle A(1, 1), B(4,2), C(1, 4). Find the parametrization, including endpoints and sketch to check. X = X1 + (x2 - X1) y = V1 + (Y2 - Y1)t Ostsi (a) A to B x(t) = 1 + (2-1) y(t) = 1+(3-1) ostsi (b) B to C x(t) = (t) = Ostsi (c) A to C X(t) = y(t) = Ostsi
Suppose that a point P1 on scanline y1 and its intensity is I1, a point P2 on scanline y2 and its intensity is I2. Please give a deduction equation on the dimension y,which can use linear interpolation calculating all the intensities I′of the points on the scanlines between P1 and P2. If P1 on scanline 5th has RGB color (1,0.5,0), P2 on scanline 15th has RGB (0.2,0.5,0.6), then what will be the color of the point on scanline 8th?
(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)...
Suppose X1, X2, . . . , Xn follows Bernoulli(p), and Y1, Y2, . . . , Ym follows Bernoulli(p + q), where both 0 < p, q < 0.5. Compute the moment estimator of p and q using first moments.
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
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...
The straight-line distance of two points (x1, y1) and (x2, y2) in a Cartesian plane can be calculated by the formula:Your task is to create an algorithm using flowchart to solve this problem. in your algorithm, you need to prompt user to enter the value of x1, x2. y1 and y2.
(d) Show that if and are distinct eigenvalues of a square matrix A, x = (x1; x2; : : : ; xn) 2 E[A], y = (y1; y2; : : : ; yn) 2 E[A] then: x; y = x1y1 + x2y2 + + xnyn = 0:
1. Suppose U(X1, X2) = 2lnx, + 3lnx, and P, = 4, P2 = 1, and m = 20. (15pts) a. Solve for the Utility maximizing amounts of x, and X2. b. Is this an interior or corner solution? c. Is the budget exhausted here? Yes/no d. Assume that the above prices and income have all doubled. How does this change your solution in a? e. Set up the Lagrangian for this problem (but do not solve it) 2. Suppose...