# A triangle has corners A, B, and C located at #(4 ,7 )#, #(3 ,5 )#, and #(6 ,2 )#, respectively. What are the endpoints and length of the altitude going through corner C?

The endpoints of altitudes

Length of the altitude going through corner C

Let

Let

Let

Slope of

Now, Slope of

So, eqn. of

from

From

Using Distance formula,

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The altitude going through corner C will be perpendicular to the side AB.

First, calculate the slope of line AB using the formula: (m = \frac{y_2 - y_1}{x_2 - x_1})

Then, find the perpendicular slope by taking the negative reciprocal of the slope of AB: (m_{\perp} = -\frac{1}{m})

Now that you have the perpendicular slope, you can find the equation of the line passing through point C with this slope. Use the point-slope form: (y - y_1 = m_{\perp}(x - x_1))

Solve for y to find the equation of the altitude.

Once you have the equation of the altitude, find its intersection point with AB. Substitute the x-coordinate of the intersection point into the equation of the altitude to find the y-coordinate.

The endpoints of the altitude will be the coordinates of corner C and the coordinates of the intersection point.

Finally, calculate the distance between the two endpoints using the distance formula: (d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2})

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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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