# In a #DeltaXYZ# having #X(-3,2)#, #Y(-5,-6)# and #Z(-5,0)#, is perpendicular bisector of #YZ# same as median from #X#?

The equations are not the same.

Find the midpoint of YZ using the midpoint formula

Since YZ is a vertical line:

The perpendicular bisector is a horizontal line:

The median from X goes from

Equation of the median

Use either the midpoint or point X to find b:

Equation of the median:

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Perpendicular bisector of

Note it is different from the equation of median given in question.

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To determine if the perpendicular bisector of YZ is the same as the median from X in triangle XYZ, we need to find the midpoint of YZ and the midpoint of XZ, then check if they coincide.

Midpoint of YZ: ((-5 - 5)/2, (-6 + 0)/2) = (-5, -3) Midpoint of XZ: ((-3 - 5)/2, (2 + 0)/2) = (-4, 1)

The perpendicular bisector of YZ passes through the midpoint of YZ (-5, -3) and is perpendicular to YZ. The slope of YZ is (-6 - 0)/(-5 + 5) = undefined.

Therefore, the perpendicular bisector of YZ is vertical, and its equation is x = -5.

The median from X passes through X and the midpoint of YZ (-5, -3). The slope of this line is (1 - (-3))/(-4 - (-5)) = 4.

The equation of the median from X is y - 2 = 4(x + 3).

Comparing the equations of the perpendicular bisector of YZ (x = -5) and the median from X (y - 2 = 4(x + 3)), they are not the same.

Thus, the perpendicular bisector of YZ is not the same as the median from X in triangle XYZ.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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