   Chapter 10.1, Problem 32E

Chapter
Section
Textbook Problem

# Use a graphing device and the result of Exercise 31(a) to draw the triangle with vertices A(1, 1), B(4, 2), and C(1, 5).

To determine

To plot: The triangle with vertices A(1,1), B(4,2) and C(1,5) and the parametric equations x=x1+(x2x1)t and y=y1+(y2y1)t.

Explanation

Given data:

The parametric equation for the variable x is as follows.

x=x1+(x2x1)t (1)

The parametric equation for the variable y is as follows.

y=y1+(y2y1)t (2)

Calculation:

For the side of the triangle AB, point (x1,y1) and (x2,y2) are A(1,1) and B(4,2), respectively.

Substitute 1 for x1 and 4 for x2 in the equation (1),

x=x1+(x2x1)t=1+(41)t=1+3t (3)

Substitute the 1 for y1 and 2 for y2 in equation (2),

y=y1+(y2y1)t=1+(21)t=1+1t=1+t (4)

For the side of the triangle BC, point (x1,y1) and (x2,y2) are B(4,2) and C(1,5), respectively

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