Practice using the coordinate plane to solve geometry problems involving distance, midpoint, slope, parallel and perpendicular lines, and equations of lines.
Read each problem carefully. Show your work in the space provided. Give exact answers when possible, and round only when the problem asks you to.
Using coordinates to analyze distance, slope, midpoint, and equations of lines
Geometry - Grade 9-12
- 1
Find the distance between A(2, -3) and B(8, 5).
- 2
Find the midpoint of the segment with endpoints P(-4, 7) and Q(6, -1).
- 3
Find the slope of the line passing through C(-2, 4) and D(3, -6).
- 4
Write the equation of the line with slope 3 that passes through the point (2, -5). Give your answer in slope-intercept form.
- 5
Determine whether the line through A(1, 2) and B(5, 10) is parallel to the line through C(-3, 4) and D(2, 14). Explain your answer.
- 6
Determine whether the line through E(-1, 3) and F(5, 6) is perpendicular to the line through G(2, -4) and H(5, -10). Explain your answer.
- 7
A triangle has vertices A(0, 0), B(6, 0), and C(6, 8). Find the lengths of all three sides and classify the triangle by its side lengths.
- 8
Find the coordinates of the point that divides the segment from A(2, 1) to B(8, 13) in a 1:2 ratio, measured from A to B.
- 9
Write the equation of the perpendicular bisector of the segment with endpoints M(-2, 4) and N(4, -2).
- 10
A quadrilateral has vertices A(-3, 1), B(1, 4), C(5, 1), and D(1, -2). Use slopes or distances to determine what type of quadrilateral it is.
- 11
Find the area of the triangle with vertices A(1, 1), B(7, 1), and C(4, 6).
- 12
The equation of a circle is (x - 3)^2 + (y + 2)^2 = 49. Identify the center and radius.
- 13
Write the equation of the circle with center (-4, 5) that passes through the point (2, 13).
- 14
A line has equation 2x - 3y = 12. Find its x-intercept and y-intercept.
- 15
A rectangle has vertices A(-2, -1), B(4, -1), C(4, 3), and D(-2, 3). Find the perimeter and area of the rectangle.