The point A(a, b) is given in the first quadrant of the coordinate plane. Draw a straight line passing through this point, which cutsfrom the first quadrant the triangle with the smallest area (See Figure). x =?,y=?YAy CA(a,b)O A. I = a, y = 2bO B. T = 2a, y = bO C. T = 2a, y = 2b%3D%3DO D. I = a, y = b

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Description: The point A(a, b) is given in the first quadrant of the coordinate plane. Draw a straight line passing through this point, which cutsfrom the first quadrant the triangle with the smallest area (See Figure). x =?,y=?YAy CA(a,b)O A. I = a, y = 2bO B.

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College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section1.1: The Coordinate Plane

Problem 34E: In these exercises we find the area of plane figures. Plot the points P(5,1),Q(0,6) and R(5,1) on a...

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The point A(a, b) is given in the first quadrant of the coordinate plane. Draw a straight line passing through this point, which cuts
from the first quadrant the triangle with the smallest area (See Figure). x =?,y=?
YA
y C
A(a,b)
O A. I = a, y = 2b
O B. T = 2a, y = b
O C. T = 2a, y = 2b
%3D
%3D
O D. I = a, y = b

Expert Solution

Step 1

Given data:

The line is passing through point A(a,b).

Step 2

The equation of line passing through point A(a,b) is given by,

$\begin{array}{rcl} (y - b) & = & m (x - a) \\ y - b & = & m x - m a \\ y - m x & = & b - m a \end{array}$

The intercept on x-axis (y=0)is given by,

$\begin{array}{rcl} y - m x & = & b - m a \\ x & = & \frac{- b + m a}{m} \end{array}$

Similarly, intercept on y-axis(x=0) is given by,

$\begin{array}{rcl} y - m x & = & b - m a \\ y & = & b - m a \end{array}$

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