# SOLUTION: Triangle ABC has vertices A (-5, 4), B (1, -2) and C (3, 6), (a)Write the equation of the line of which AB is a segment. (b)Write the equation of the line of which the altitude t

Algebra ->  Algebra  -> Triangles -> SOLUTION: Triangle ABC has vertices A (-5, 4), B (1, -2) and C (3, 6), (a)Write the equation of the line of which AB is a segment. (b)Write the equation of the line of which the altitude t      Log On

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 Geometry: Triangles Solvers Lessons Answers archive Quiz In Depth

 Question 332266: Triangle ABC has vertices A (-5, 4), B (1, -2) and C (3, 6), (a)Write the equation of the line of which AB is a segment. (b)Write the equation of the line of which the altitude to line AC is a segment. (c)Write the equation of the perpendicular bisector of line AC. (d)Find the perimeter of triangle ABC.Found 2 solutions by D'Leeter, Edwin McCravy:Answer by D'Leeter(4)   (Show Source): You can put this solution on YOUR website! (a). Use the two-point form of an equation of a line: where and are the coordinates of points A and C. (b). Step 1. Use the portion of the two-point form to determine the slope of the line containing segment AB. Step 2: Calculate the negative reciprocal of the slope determined in Step 1 because: Step 3: Use the point-slope form of an equation of a line: where are the coordinates of point C and is the slope calculated in (b) Step 2. (c) Step 1: Use the mid-point formulas: and where and are the coordinates of points A and C to calculate the midpoint of segment AC. Use the slope calculated in (b) Step 2 and the midpoint calculated in (c) Step 1 with the point-slope form to derive the equation of the perpendicular bi-sector of AC. (d) Step 1: Use the distance formula 3 times: where , , and are the coordinates of points A, B, and C . Step 2: Sum the three results. John My calculator said it, I believe it, that settles it Answer by Edwin McCravy(8999)   (Show Source): You can put this solution on YOUR website! Triangle ABC has vertices A (-5, 4), B (1, -2) and C (3, 6),  That triangle is:  (a)Write the equation of the line of which AB is a segment.  That's the green line below:  (b)Write the equation of the line of which the altitude to line AC is a segment.  That's the blue line below: Since it is an altitude, it is perpendicular to AC. First we find the slope of AC: The blue line is perpendicular to AC so its slope is the reciprocal of with the opposite sign, so the blue line's slope is and it passes through B(1,-2)  (c) Write the equation of the perpendicular bisector of line AC.  We find the midpoint of AC, using the midpoint formula: Midpoint = (,) = (,) = (,) = M(-1,5) Now we find the equation of the red line through M(-1,5), it has the same slope as the altitude since both are perpendicular to the line AC. The red line's slope is also but it passes through M(-1,5)  (d)Find the perimeter of triangle ABC.  We use the distance formula to find the lengths of all three sides. So the perimeter = AB + BC + AC = Edwin