A triangle has corners A, B, and C located at #(3 ,4 )#, #(2 ,5 )#, and #(2 , 1 )#, respectively. What are the endpoints and length of the altitude going through corner C?
Length of altitude
End points of altitude from vertex
Now, the length of altitude CN is given by distance formula
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To find the endpoints of the altitude going through corner C, you first need to determine the equation of the line containing side AB. Then, find the perpendicular line passing through C. The intersection point of these two lines will give you the endpoints of the altitude. Finally, calculate the distance between this intersection point and corner C to find the length of the altitude.

Calculate the slope of line AB using the formula: slope = (y2  y1) / (x2  x1). Slope of AB = (5  4) / (2  3) = 1 / 1 = 1.

Use the pointslope form of a line to find the equation of line AB. Choose any point on AB. Using (3, 4): y  4 = 1(x  3) y  4 = x + 3 y = x + 7.

The slope of a line perpendicular to AB is the negative reciprocal of the slope of AB. So, the slope of the altitude is 1.

Using the pointslope form of a line with slope 1 passing through point C(2, 1): y  1 = 1(x  2) y  1 = x  2 y = x  1.

Solve the system of equations formed by equating the equations of lines AB and the perpendicular line: x + 7 = x  1 2x = 8 x = 4.

Substitute x = 4 into either equation to find y: y = 4  1 = 3.

The intersection point is (4, 3), which is the endpoint of the altitude.

Calculate the distance between (4, 3) and C(2, 1) using the distance formula: Distance = √((x2  x1)^2 + (y2  y1)^2) = √((4  2)^2 + (3  1)^2) = √(2^2 + 2^2) = √8 = 2√2.
Therefore, the endpoints of the altitude going through corner C are (4, 3) and the length of the altitude is 2√2.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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