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Applications of Midpoint and Length of A Line Segment

Applications of Midpoint and Length of A Line Segment. Example 1: Determine the shortest distance from the line 4x – 2y = 8 to the point (-2,6). STEP 1: Determine the slope of the shortest line that joins (-2,6) to the line 4x – 2y = 8, knowing that it is perpendicular to the given line.

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Applications of Midpoint and Length of A Line Segment

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  1. Applications of Midpoint and Length of A Line Segment

  2. Example 1: Determine the shortest distance from the line 4x – 2y = 8 to the point (-2,6). • STEP 1: Determine the slope of the shortest line that joins (-2,6) to the line 4x – 2y = 8, knowing that it is perpendicular to the given line.

  3. Example 1: Determine the shortest distance from the line 4x – 2y = 8 to the point (-2,6). • STEP 2: Determine the equation of the line that joins (-2,6) to the line • 4x – 2y = 8

  4. Example 1: Determine the shortest distance from the line 4x – 2y = 8 to the point (-2,6). • STEP 3: Determine the point of intersection D of the two lines using an algebraic method.

  5. Example 1: Determine the shortest distance from the line 4x – 2y = 8 to the point (-2,6). • STEP 4: Determine the distance between (-2,6) and the point of intersection D found in step 3.

  6. Example 2: Given the triangle joining the points A(-5,2), B(2,4) and C(3,-4), prove that the line segment joining the midpoints of AB and BC is parallel to AC • STEP 1: Determine the midpoints of AB and BC

  7. Example 2: Given the triangle joining the points A(-5,2), B(2,4) and C(3,-4), prove that the line segment joining the midpoints of AB and BC is parallel to AC • STEP 2: Determine the slopes of MN and AC.

  8. Example 3: Prove that the triangle joining the points S(5,5) T(-3,-1) and U(1,-3) is a right triangle. • Method 1: • Using slopes.

  9. Example 3: Prove that the triangle joining the points S(5,5) T(-3,-1) and U(1,-3) is a right triangle. • Method 2: • Using lengths.

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