A is the point (-1, 5). Let (x, y) be any point on the line y = 3x.
a Write an equation in terms of x for the distance between (x, y) and A(-1,5).
b Find the coordinates of the two points, B and C, on the line y = 3x which are a distance of √74 from (-1,5).
c Find the equation of the line l1 that is perpendicular to y = 3x and goes through the point (-1,5).
d Find the coordinates of the point of intersection between l1, and y = 3x.
e Find the area of triangle ABC.
3. What point on the line y = 7 - 3x is closest to the origin? a. Sketch the line carefully and mark the point on the line that you think is closest to the origin. b. Write the distance between the origin and a point (x,y) in the plane. If you don't know, think of a triangle with base x and height y. 8 7 6 c. The point must be on the line, so you can write the...
Find the equation of the line perpendicular to 3x+y-2=0 that goes through the point, (0,1) Show all work.
Additional problem 1 Let AABC be a triangle, let be the bisector of the angle ZCAB Let P be the intersection of and BC. Let R be the point on the line AB such that AR-AC, and let X-APnRC. Let Q denote the intersection point between the line through B and X and AC. (a) Show that the triangle AARC is isosceles, and deduce that RX-XC. (b) Apply Menelaus's theorem to the triangle AARC with the line through B, X,...
Find the point on the line y - 3x + 5 closest to the point (1,3). The function giving the distance between the point and the line is 8 (Enter a function of 2) (Enter the coordinates of the point. Be The point closest to the line is sure to include commas and parentheses as required.
5. Let R be the region bounded by the graph of, y Inr + 1) the line y 3, and the line x - 1. (a)Sketch and then find the area of R (b) The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is an equilateral triangle. (c) Another solid whose base is also the region R. For this solid, each cross section perpendicular to the x-axis is a Semi-circle...
Question 15 The curve with the equation y = 3x + 2x + 5 is shown below. (-1,0) 0 x The curve cuts the x axis at the point A(-1,0) and cuts the y axis at point 8 a) State the coordinates of Point B and hence find the area of the triangle AOB (3 marks) b) Find 3x5 + 2x + 5 dx (3 marks) c) Find the area of the shaded region bounded by the curve and the...
please help me through these questions for a area of a rectangle In this problem, we'll walk through the steps to find the area of the rectangle bounded by: The line f(x) = 3z + 8 The line g(x) parallel to f(x) passing through the point(0,3) The line h(z) perpendicular to f(z) passing through (26,0) The line j(x) perpendicular to f(x) passing through (0,8) bility a) Find the equation for the line g(x) 9(z) = Preview b) Find the equation...
5. (a) Let u 1,4,2), ,1,0). Find the orthogonal projection of u on v (b) Letu ,1,0), u(0,1,1), (10,1). Find scalars c,,s such that 6. (a) Find the area of the triangle with vertices , (2,0,1), (3, 1,2). Find a vector orthogonal to the plane of the triangle. (b)) Find the distance between the point (1,5) and the line 2r -5y1 (i) Find the equation of the plane containing the points (1,2, 1), (2,1, 1), (1, 1,2). 7. (a) Let...
Find an equation for the line perpendicular to y=(-1/10)x + 3 and goes through the point (4,9). Write your answer in the form y = mx + b. y = _______
Let C be a triangle in the x-y plane with vertices (x1,y1), (x2y2) and (x3,y3) arranged so that C is positively-oriented. Let C be a triangle in the xy-plane with vertices (x,y), (z2,p), and (z3,U3) arranged so that C is positively-oriented. a.) Sketch such a triangle and indicate its orientation. b.) Apply Green's Theorem to compute the area of the triangle as a (sum of) path integral(s) around the boundary. Get a formula for area in terms of the coordinates...
> I think the roots of the quadratic equation should be 4 and -1.2
Victor Onyango Oketch Mon, Jan 3, 2022 9:01 PM