Problem 1034 Find the distance between the gi... [FREE SOLUTION]

Chapter 32: Problem 1034

Find the distance between the given pair of points, and find the slope of the line segment joining them. \((3,-5),(2,4)\)

Short Answer

Expert verified

The distance between the given pair of points (3, -5) and (2, 4) is \(\sqrt{82}\), and the slope of the line segment joining them is -9.

Step by step solution

First, we need to identify the coordinates of the two points. The first point (Point A) has coordinates (3, -5) which means its x-coordinate is 3 and its y-coordinate is -5. The second point (Point B) has coordinates (2, 4) which means its x-coordinate is 2 and its y-coordinate is 4. #Step 2: Use the distance formula to find the distance between the points#

The distance formula is as follows: Distance = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\) Plug in the coordinates of the points into this formula: Distance = \(\sqrt{((2 - 3)^2 + (4 - (-5))^2)}\) #Step 3: Calculate the distance between the points#

Now, we'll carry out the arithmetic operations in the distance formula: Distance = \(\sqrt{((-1)^2 + (9)^2)}\) Distance = \(\sqrt{(1 + 81)}\) Distance = \(\sqrt{82}\) So, the distance between the two points is \(\sqrt{82}\). #Step 4: Use the slope formula to find the slope of the line segment#

The slope formula is as follows: Slope = \(\frac{(y_2 - y_1)}{(x_2 - x_1)}\) Plug in the coordinates of the points into this formula: Slope = \(\frac{(4 - (-5))}{(2 - 3)}\) #Step 5: Calculate the slope of the line segment#

Now, we'll carry out the arithmetic operations in the slope formula: Slope = \(\frac{(4 + 5)}{-1}\) Slope = \(\frac{9}{-1}\) Slope = -9 So, the slope of the line segment is -9. #Final answer#

The distance between the given pair of points (3, -5) and (2, 4) is \(\sqrt{82}\), and the slope of the line segment joining them is -9.

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91影视

Find the distance between the given pair of points, and find the slope of the line segment joining them. \((3,-5),(2,4)\)

Short Answer

Step by step solution

Now, we'll carry out the arithmetic operations in the distance formula: Distance = \(\sqrt{((-1)^2 + (9)^2)}\) Distance = \(\sqrt{(1 + 81)}\) Distance = \(\sqrt{82}\) So, the distance between the two points is \(\sqrt{82}\). #Step 4: Use the slope formula to find the slope of the line segment#

Now, we'll carry out the arithmetic operations in the slope formula: Slope = \(\frac{(4 + 5)}{-1}\) Slope = \(\frac{9}{-1}\) Slope = -9 So, the slope of the line segment is -9. #Final answer#

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