2. Reflect on and relate coordinate and direct proofs of somegeometric theorems. Try to construct coordinate proofscorresponding to direct proofs of other theorems and/orcorollaries involving properties of geometric figures likepolygons and circles.

The coordinate proof is a proof of a geometric theorem which uses "generalized" points on the…

Answered: 2. Reflect on and relate coordinate and…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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(a) If the abscissa and ordinates of two points P and Q are the roots ofthe equations x\power{2}+2ax-b\power{2}=0 and x\power{2}+2px-q\power{2}=0 respectively,then find the equation of the circle with PQ as diameter. (b)Find the equation of the circle which passes through (1, 0) and (0, 1) and has its radius as small as possible.
I need to find the distance of y in the diagram. I've been told that the radius of the circle is 100ft and that the angle theta is 30 degrees. I'm having a hard time setting up my equation. I'm trying to use the pythagorean theorem though I can't find a way to make all of variables in terms of a single variable. Since I know that in a 30-60-90 triangle the hypotuse is equal to 2t, the medium length leg is equal to t(radical 3) and the smallest leg is "t," I've tried setting up the following t=(100+x)/2 for the hypotnuse and t=((14+b)(radical 3))/3 for the meduim length leg. Though, I can't put this into the pythagorean theorem and solve it because I still have two unknown variables. Am I setting the problem up right?
Part B needed in 10 minutes and get the thumbs up please take only 10 minutes
1. The center of a circle is the point C(5,4). The circle touches the y-axis at the point D and intersects the x-axis at the points A and 8, with A being closer to the y-axis than B. (a) Write down the general equation of the circle. (b) State the coordinates of D and find the coordinates of A and B. (c) () Find the equation of the locus of the point P such that the distance from P to D is twice the distance from P to A (PD=2PA).
See the diagram below. In this diagram plane 1 and plane 2 are parallel. Point Q (0, 2, 7) is on plane 1 and point P (1, - 3, 7) is on plane 2. The equation of plane 2 is 2x + hy + kz=10. Find the distance between plane 1 and plane 2 in terms of h and k. Label your graph and show all work, please don't just plug numbers into a formula. Hint, you can use vector projections/a dot product. Plane 2: . P (1, -3, 7) Plane 1: . Q (0, 2, 7)
C. For any three noncollinear points, there is exactly one circle that passes through all them. Thus, if we are given three such points, it should be possible to find an equation for the circle. 1. A circle passes through P(5,9), Q(11,-3), and R(13,3). Find its equation in the standard form. 2 A circle passes through A(3,6), B(-5,10), and C(-2,1). Find its equation in the standard form. YWord prohlem

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2. Reflect on and relate coordinate and direct proofs of some geometric theorems. Try to construct coordinate proofs corresponding to direct proofs of other theorems and/or corollaries involving properties of geometric figures like nolygons and circles.