Question 1: The two shorter sides of a right triangle ABC are on the coordinate axes and its hypotenuse passes through the point (1,8): A (1,8) в We are interested in finding the vertices A and C such that the length of the hypotenuse is minimum. Lets us do it as follows: (a) Write the equation of a straight line whose slope is m and which passes through the point (1,8). (b) Find out the x-intercept and y-intercept of the line in (a) in terms of the slope m. (c) Let us denote the length of the hypotenuse AC as h. h is a function of the slope m. Show that m h(m) : + (8— т)2 (d) With our current knowledge of calculus, it is difficult to find m that minimizes h(m). So instead of minimizing h(m), let us minimize r(m) = h°(m). This will not change the location of the minimum m. To convince yourself graph both h(m) and r(m) = h°(m). Where do you locate the minimum? (e) Now show that 2. 64 16 + 65 m m - - 8 r(m) + (8— т)? — т? + 16т m m2

Question 1: The two shorter sides of a right triangle ABC are on the coordinate axes and its hypotenuse passes through the point (1,8): A (1,8) в We are interested in finding the vertices A and C such that the length of the hypotenuse is minimum. Lets us do it as follows: (a) Write the equation of a straight line whose slope is m and which passes through the point (1,8). (b) Find out the x-intercept and y-intercept of the line in (a) in terms of the slope m. (c) Let us denote the length of the hypotenuse AC as h. h is a function of the slope m. Show that m h(m) : + (8— т)2 (d) With our current knowledge of calculus, it is difficult to find m that minimizes h(m). So instead of minimizing h(m), let us minimize r(m) = h°(m). This will not change the location of the minimum m. To convince yourself graph both h(m) and r(m) = h°(m). Where do you locate the minimum? (e) Now show that 2. 64 16 + 65 m m - - 8 r(m) + (8— т)? — т? + 16т m m2

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter9: Quadratic Functions And Equations

Section9.7: Solving Systems Of Linear And Quadratic Equations

Problem 21PPS

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Three of the four vertices of a parallelogram are 0,-2, 6,8, and 10,1. Find the possibilities for the coordinates of the remaining vertex.
Is the point (0,8) on the x-axis or y-axis? How do you know?
Find the equation of the line perpendicular to the line y=3 and passing through the midpoint of the segment joining 2, 4 and -6, 10.

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