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Point C has the coordinates [tex](-1, 4)[/tex] and point D has the coordinates [tex](2, 0)[/tex]. What is the distance between points C and D?

[tex]\[ d = \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2} \][/tex]

[tex]\[\boxed{\text{units}}\][/tex]

Sagot :

GinnyAnsweridn
Certainly! Let's calculate the distance between points C and D step-by-step using the distance formula:

The coordinates of point C are [tex]\((-1, 4)\)[/tex], and the coordinates of point D are [tex]\((2, 0)\)[/tex]. The distance formula between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:

[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]

Substitute the coordinates of points C and D into the formula:
- [tex]\(x_1 = -1\)[/tex]
- [tex]\(y_1 = 4\)[/tex]
- [tex]\(x_2 = 2\)[/tex]
- [tex]\(y_2 = 0\)[/tex]

Now, calculate the difference in the [tex]\(x\)[/tex]-coordinates ([tex]\(x_2 - x_1\)[/tex]) and [tex]\(y\)[/tex]-coordinates ([tex]\(y_2 - y_1\)[/tex]):

[tex]\[ x_2 - x_1 = 2 - (-1) = 3 \][/tex]

[tex]\[ y_2 - y_1 = 0 - 4 = -4 \][/tex]

Next, square these differences:

[tex]\[ (x_2 - x_1)^2 = 3^2 = 9 \][/tex]

[tex]\[ (y_2 - y_1)^2 = (-4)^2 = 16 \][/tex]

Add these squared differences together:

[tex]\[ (x_2 - x_1)^2 + (y_2 - y_1)^2 = 9 + 16 = 25 \][/tex]

Finally, take the square root of the sum to find the distance:

[tex]\[ d = \sqrt{25} = 5 \][/tex]

Therefore, the distance between points C and D is [tex]\(\boxed{5}\)[/tex] units.
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