Let AABC be inscribed in a semicircle with diameter AB such that C is on the circumference((r,0),of the semicircle as illustrated below. If the center of the circle is the origin, the point A =!!the point B= (r,0) and the x-coordinate of the point C is x, then C= (x, Vr2 – x2)!!(1) Find the slopes of AC and BC.(2) Show that AC I BC. (Hint: It may be helpful to recall that (a + b)(a - b) = a? - b²).CAApr 22, 2022, 12:56 PM

Answered: Image /qna-images/answer/efa3fc96-b9f1-4ced-ba06-ececc0bbb1e8.jpg

Let AABC be inscribed in a semicircle with diameter AB such that C is on the circumference of the semicircle as illustrated below. If the center of the circle is the origin, the point A = = (-r,0), (r,0) and the x-coordinate of the point C is x, then C= (x, vr2 - x2). !! the point B (1) Find the slopes of AC and BC. (2) Show that AC 1 BC. (Hint: It may be helpful to recall that (a + b) (a - b) = a² – b²). Apr 22, 2022, 12:56 PM

Let AABC be inscribed in a semicircle with diameter AB such that C is on the circumference of the semicircle as illustrated below. If the center of the circle is the origin, the point A = = (-r,0), (r,0) and the x-coordinate of the point C is x, then C= (x, vr2 - x2). !! the point B (1) Find the slopes of AC and BC. (2) Show that AC 1 BC. (Hint: It may be helpful to recall that (a + b) (a - b) = a² – b²). Apr 22, 2022, 12:56 PM

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.2: Graphs Of Linear Equations And Slope

Problem 41E: Quadrilateral EFGH has the vertices E0,0, Fa,0, Ga+b,c, and H2b,2c. Verify that EFGH is a trapezoid...

See similar textbooks

Similar questions

Quadrilateral EFGH has the vertices E0,0, Fa,0, Ga+b,c, and H2b,2c. Verify that EFGH is a trapezoid by showing that the slopes of two sides are equal.
A curve on the xy-plane passes through the point (0, a) for some number a, and has the propertythat the slope of the curve at every point P is three times the y-coordinate of P. Find theequation of the curve.
Find the slope and concavity of the curves at the given points. r = θ, θ = 0, π/2
Find the shortest distance from the origin to the line of intersection of the planes 2x + y − z = 1 and x − y + z = 2.
Find an equation for the set of points in an xy-plane that are equidistant from the point P and the line l.P(-6, 3); l: x = -2
Find an equation of the curve in the xy-plane that passes through the point (2, 3) and has, at every point (x, y) on it, slope 2x/(1 + y^2 ). Explain your answer.
Prove that the curves y2 = 4x and x2+ y2-6x+1 = 0 touch each other at the point (1,2)
The shortest distance from the point P ( 2 , 2 , 0 ) to the plane 3 x − 4 y − 5 z − 2 = 0 is given by
Let S be the graph of f(x, y) = x2 + y2 - 2x + y for(x, y) ∈ D = {(x, y) : x2 + y2 ≤ 4 and x + y ≥ 0}. Let C1 be the curve along the edge of the graph of fover the straight edge of D – starting in the secondquadrant and ending in the fourth quadrant of D • Let C2 be the curve along the edge of the graph of fover the circular edge of D – starting in the secondquadrant and ending in the fourth quadrant of D. Let F(x, y, z) = ⟨x, y, y z⟩ Compute R: C1 F¯ · dr¯.
Find the point closest to the origin on the line of intersection of the planes y + 2z = 12 and x + y =6.
Given the function f 1x2 = 1 - cos x and the points A1p>2, f 1p>222, B1p>2 + 0.05, f 1p>2 + 0.0522, C1p>2 + 0.5, f 1p>2 + 0.522, and D1p, f 1p22 (see figure), find the slopes of the secant lines through A and D, A and C, and A and B. Then use your calculations to make a conjecture about the slope of the line tangent to the graph of f at x = p>2.
a. Tangents are drawn from any point on the line x + 4a = 0 to the parabola y2 = 4ax. Then find the angle subtended by the chord of contact at the vertex. b.if the chord of contact of tangents from a point P to the parabola y2 = 4ax touches the parabola x2 = 4by, then find the locus of P.