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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2) The point P(x, –) lies on the unit circle in quadrant III. Find its x co-ordinate. Page 1 of 5
(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.
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.