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

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

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



Answer :

GinnyAnswer
To find the distance between the two points [tex]\( C \)[/tex] and [tex]\( D \)[/tex], we can use the distance formula:

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

Here, the coordinates of point [tex]\( C \)[/tex] are [tex]\((-1, 4)\)[/tex], and the coordinates of point [tex]\( D \)[/tex] are [tex]\((2, 0)\)[/tex]. Let's break it down step by step:

1. Identify the coordinates:
- Point [tex]\( C \)[/tex] ( [tex]\( x_1, y_1 \)[/tex] ) = [tex]\((-1, 4)\)[/tex]
- Point [tex]\( D \)[/tex] ( [tex]\( x_2, y_2 \)[/tex] ) = [tex]\((2, 0)\)[/tex]

2. Calculate the differences in the x and y coordinates:
- [tex]\( \Delta x = x_2 - x_1 = 2 - (-1) = 3 \)[/tex]
- [tex]\( \Delta y = y_2 - y_1 = 0 - 4 = -4 \)[/tex]

3. Square each difference:
- [tex]\( (\Delta x)^2 = 3^2 = 9 \)[/tex]
- [tex]\( (\Delta y)^2 = (-4)^2 = 16 \)[/tex]

4. Sum the squares of the differences:
- [tex]\( (\Delta x)^2 + (\Delta y)^2 = 9 + 16 = 25 \)[/tex]

5. Take the square root of the sum to find the distance:
- [tex]\( d = \sqrt{25} = 5 \)[/tex]

So, the distance between points [tex]\( C \)[/tex] and [tex]\( D \)[/tex] is [tex]\( 5 \)[/tex] units.

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