Write an equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5)

9514 1404 393

  2x +y = -2

Step-by-step explanation:

The bisector must have a slope that is the negative reciprocal of the slope of the line between these points. It must pass through the midpoint of the segment.

The slope of the line through the given points is ...

  m = (y2 -y1)/(x2 -x1)

  = (5 -(-1))/(4 -(-8)) = 6/12 = 1/2

The slope of the required bisector is then ...

  m = -1/(1/2) = -2

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The midpoint of the given segment is ...

  ((-8, -1) +(4, 5))/2 = (-8+4, -1+5)/2 = (-4, 4)/2 = (-2, 2)

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Then the point-slope form of the equation of the bisector is ...

  y -y1 = m(x -x1)

  y -2 = -2(x -(-2))

  y = -2x -4 +2

  y = -2x -2 . . . . . . . slope-intercept form equation

  2x +y = -2 . . . . . . . standard form equation

25/4

step-by-step explanation:

call segment cd's length x. because dc and ab are parallel, angle acd and cab, so triangles adc and abc are similar and we can set up the equation x / ac = ac / ab, or x / 5 = 5 / 4 and x = 25/4.

the first question mark is 6 and the second question mark is 26 (the square root)

step-by-step explanation: