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Problem 627

# Find the distance between the point $$\mathrm{C}(-3,-2)$$ and the point $$\mathrm{D}(-3,4)$$

Expert verified
The distance between points C(-3, -2) and D(-3, 4) is 6 units.
See the step by step solution

## Step 1: Identify the given points

The given points are C(-3, -2) and D(-3, 4).

## Step 2: Calculate the horizontal distance between points C and D

The x-coordinates of points C and D are both -3, so the horizontal distance between the points is 0.

## Step 3: Calculate the vertical distance between points C and D

The y-coordinate of point C is -2 and the y-coordinate of point D is 4. So, the vertical distance between the points is 4 - (-2) = 6.

## Step 4: Apply the distance formula

Since the horizontal distance is 0 and the vertical distance is 6, we can apply the distance formula to find the distance between points C and D: $d=\sqrt{(horizontal\:distance)^2+(vertical\:distance)^2}$ $d=\sqrt{(0)^2+(6)^2}$

## Step 5: Calculate the distance between points C and D

Calculate the distance by plugging the values into the above distance formula: $d=\sqrt{(0)^2+(6)^2}=\sqrt{0+36}=\sqrt{36}$ The distance between points C and D is 6 units.

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