Draw the triangle with vertices D(-2,1), U(4,9), and E(10,1) On a Graph.
2. Find DU, UE, AND DE. (Distance)
3. Classify Triangle DUE by its sides.
4. Write the standard form of the equation of each line: DU, UE, and DE.Also, find the slode and then the y-intercept. Start with y=mx+b and move into standard form.
5. Draw the altitude from U to DE.Name it UM
6. What is the equation of the line UM?
7. Find the Midpoint of UE. Write the formula.Name the midpoint O on your diagram.
8. Write the equation of DO in standard form
9. Find the midpoint of DU.
10. Write the standard form of the equation of line EN.
11. Find the Measure of angle EUM using trigonomotry. Round to the nearest tenth.
12. If you rotated triangle DUE 270 degrees CLOCKWISE, what would the new cordinates be?
13. Write the standard form of the equation of the perpindicular bisector of DU.
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To answer the questions, follow these steps:
1. Start by drawing a graph on a coordinate plane. Mark the points D(-2,1), U(4,9), and E(10,1) as shown.
2. To find the distances DU, UE, and DE, use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
For DU: Distance = sqrt((4 - (-2))^2 + (9 - 1)^2)
= sqrt(6^2 + 8^2) = sqrt(36 + 64) = sqrt(100) = 10
Similarly, find the distances UE and DE.
3. To classify Triangle DUE by its sides, measure the three distances you just found. Since DU = DE < UE, the triangle is an isosceles triangle.
4. To find the equations of the lines DU, UE, and DE, first, find the slope using the formula:
Slope (m) = (y2 - y1) / (x2 - x1)
Using point-slope form (y - y1) = m(x - x1), you can convert it into slope-intercept form (y = mx + b).
For example, to find the equation of DU:
Slope (m) = (9 - 1) / (4 - (-2)) = 8 / 6 = 4 / 3
Using point-slope form, y - 1 = (4/3)(x - (-2)) simplifies to y - 1 = (4/3)(x + 2)
Rearranging to slope-intercept form, y = (4/3)x + (8/3)
Find the slopes and equations in a similar manner for UE and DE.
5. To draw the altitude UM from U to DE, first, find the slope of DE (call it m1). Then the slope of the line perpendicular to DE is the negative reciprocal of m1. Find a point on DE, and use point-slope form to find the equation of UM.
6. To find the equation of line UM, use the slope-intercept form (y = mx + b) or point-slope form.
7. To find the midpoint of UE, use the midpoint formula:
Midpoint (x, y) = ((x1 + x2) / 2 , (y1 + y2) / 2)
Substitute the coordinates of U and E into the formula to find the midpoint. Name it O on the diagram.
8. To write the equation of DO in standard form, first find the slope using the midpoint formula for DO. Then use the point-slope form to write the equation. Finally, convert it to standard form (Ax + By = C).
9. To find the midpoint of DU, again use the midpoint formula by substituting the coordinates of D and U. Name it midpoint P on your diagram.
10. To write the standard form of the equation of line EN, first find the slope using the coordinates of E and N, then use the point-slope form. Finally, convert it to standard form (Ax + By = C).
11. To find the measure of angle EUM using trigonometry, use the Law of Cosines or the inverse trigonometric functions. These calculations depend on the lengths of the sides of the triangle DUE, which you found in question 2.
12. To rotate triangle DUE 270 degrees clockwise, apply the rotation rules to each coordinate point. The new coordinates will be the result of rotating (-2,1), (4,9), and (10,1) around the origin.
13. To write the standard form of the equation of the perpendicular bisector of DU, first, find the midpoint of DU (P). Then find the slope of DU (m1) and the negative reciprocal (m2). Using the point-slope form, write the equation of the perpendicular bisector. Finally, convert it to standard form (Ax + By = C).
Remember to consult a graphing tool or calculator if needed to check your answers, as the accuracy of the diagram and calculations is crucial for the correct answers.