Mid-Chapter Quiz: Lessons 9-1 through 9-4. Find the midpoint of the line segment with endpoints at the given coordinates (7, 4), ( 1, 5)
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1 Find the midpoint of the line segment with endpoints at the given coordinates (7, 4), (1, 5) Let (7, 4) be (x 1, y 1 ) and (1, 5) be (x 2, y 2 ). (2, 9), (6, 0) Let (2, 9) be (x 1, y 1 ) and (6, 0) be (x 2, y 2 ). HIKING Carla and Lance left their campsite and hiked 6 miles directly north and then turned and hiked 7 miles east to view a waterfall. a. How far is the waterfall from their campsite? b. Let the campsite be located at the origin on a coordinate grid. At the waterfall they decide to head directly back to the campsite. If they stop halfway between the waterfall and the campsite for lunch, at what coordinate will they stop for lunch? a. The coordinate of their campsite is (0, 0) and the coordinate of the waterfall is (7, 6). Let (0, 0) be (x 1, y 1 ) and (7, 6) be (x 2, y 2 ). Find the distance between each pair of points with the given coordinates (0, 6), (2, 5) Let (0, 6) be (x 1, y 1 ) and (2, 5) be (x 2, y 2 ). (10, 1), (0, 4) Let (10, 1) be (x 1, y 1 ) and (0, 4) be (x 2, y 2 ). b. Let (0, 0) be (x 1, y 1 ) and (7, 6) be (x 2, y 2 ). Write each equation in standard form. Identify the vertex, axis of symmetry, and direction of opening of the parabola. vertex: (2, 9) axis of symmetry: x = 2 The graph opens up. N esolutions Manual - Powered by Cognero Page 1
2 BRIDGES Write an equation of a parabola to model the shape of the suspension cable of the bridge shown. Assume that the origin is at the lowest point of the cables. vertex: (4, 1) axis of symmetry: y = 1 The graph opens right. vertex: (12, 80) axis of symmetry: x = 12 The graph opens up. The vertex of the parabola is (0, 0). So, h = 0 and k = 0. It passes through the coordinates (250, 200) and (250, 200). Substitute (250, 200) in the standard form of the equation and find a. Therefore, the equation of a parabola to model the shape of the suspension cable is. Identify the coordinates of the vertex and focus, vertex: axis of symmetry: y = The graph opens right. B D S esolutions Manual - Powered by Cognero Page 2
3 Identify the coordinates of the vertex and focus, the equation of the axis of symmetry and directrix, and the direction of opening of the parabola with the given equation. Then find the length of the latus rectum. Find the center and radius of the circle with equation The center of the circle is (1, 0).. Then graph the circle. vertex: (3, 4) Focus: axis of symmetry: x = 3 directrix: The graph opens up. Write an equation for a circle that has center at (3, 2) and passes through (3, 4). Distance between the coordinates (3, 2) and (3, 4): length of the latus rectum: 1 unit The equation of the circle is. Write an equation for a circle if the endpoints of a vertex: (3, 1) focus: axis of symmetry: y = 1 directrix: The graph opens left. length of the latus rectum: Find the center and radius of the circle with esolutions Manual - Powered by Cognero Page 3
4 Write an equation for a circle if the endpoints of a diameter are at (8, 31) and (32, 49). Midpoint of (8, 31) and (32, 49): The center of the circle is (20, 40). Distance between (20, 40) and (32, 49): Find the coordinates of the center and foci and the lengths of the major and minor axes of the ellipse with the given equation. Then graph the ellipse. The center of the ellipse is (4, 2), so h = 4 and k = 2. a 2 = 16 and b 2 = 9 The equation of the circle is MULTIPLE CHOICE What is the radius of the circle with equation? A B 4 C 8 D 16. Thus, the coordinates of the foci are The length of the major axis is 2a which is 8 units. The length of the minor axis is 2b which is 6 units.. The radius of the circle is 4 units. Find the coordinates of the center and foci and esolutions Manual - Powered by Cognero Page 4
5 The center of the ellipse is (1, 2), so h = 1 and k = 2. a 2 = 20 and b 2 = 4 Thus, the coordinates of the foci are (5, 2) and (3, 2). The length of the major axis is 2a which is The length of the minor axis is 2b which is 4 units. The center of the ellipse is (5, 2), so h = 5 and k = 2. a 2 = 9 and b 2 = 4 Thus, the coordinates of the foci are The length of the major axis is 2a which is 6 units. The length of the minor axis is 2b which is 4 units.. MULTIPLE CHOICE esolutions Manual - Powered by Cognero Page 5
6 MULTIPLE CHOICE Which equation represents an ellipse with endpoints at (4, 10) and (4, 6) and foci at about (4, 7.3) and (4, 3.3)? F G H I The x-coordinates are the same for both vertices, so the ellipse is vertical. The center of the ellipse is at or (4, 2), so h = 4 and k = 2. The length of the major axis is 2a = 16, so a = 8, and a 2 = 64. The focus is at (h, k c), so 2 + c = 7.3, and c = 5.3. Use the values of a and c to find b. So, the equation for this ellipse is esolutions Manual - Powered by Cognero Page 6
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