8. Self-Test
Answers to the questions are available at the end of the book.
- Three vertices of a rectangle ABCD have the points A (–3, 4), B (5, 4), and C (5, –1). Find the coordinates of the 4th vertex, and determine the area of the rectangle. (Hint: Area of a [latex]rectangle = length \times width[/latex])
- Write the following equations in standard form:
a. [latex]\displaystyle{y = \frac{2}{3}x - 2}[/latex]
b. [latex]\displaystyle{6 - 2x + \frac{1}{4} = 0}[/latex] - Write the following equations in slope-intercept form:
a. [latex]2x - 3y + 6 = 0[/latex]
b. [latex]3x + 4y - 5 = 0[/latex] - Graph the equation [latex]2x - 3y = 9[/latex] using a table of values with 4 points.
- Graph the equation [latex]3y + 4x = 0[/latex] using the x-intercept, y-intercept, and another point on the line.
- Use the following slopes (m) and y-intercepts (b) to graph the equations:
a. [latex]\displaystyle{m = -\frac{1}{2}}[/latex], [latex]b = -4[/latex]
b. [latex]\displaystyle{m = \frac{2}{3}}[/latex], [latex]b = -2[/latex] - Determine the equation of the line, in standard form, that passes through the points P (–4, 5) and Q (1, 1).
- Determine the equation of the line, in standard form, having an x-intercept equal to 5 and a y-intercept equal to –3.
- Determine the equation of a line, in standard form that is parallel to [latex]3x - 2y + 9 = 0[/latex] and that passes through the point (–6, –3).
- Determine the equation of the line, in standard form, that passes through the origin and is perpendicular to the line passing through the points P(–3, 5) and Q(5, –1).
Unless otherwise indicated, this chapter is an adaptation of the eTextbook Foundations of Mathematics (3rd ed.) by Thambyrajah Kugathasan, published by Vretta-Lyryx Inc., with permission. Adaptations include supplementing existing material and reordering chapters.
