Question

Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(5, 5),A(5,5),A, left parenthesis, 5, comma, 5, right parenthesis, comma B(7,5)B(7,5)B, left parenthesis, 7, comma, 5, right parenthesis, C(7,-1)C(7,−1)C, left parenthesis, 7, comma, minus, 1, right parenthesis, and D(5,-1)D(5,−1)D, left parenthesis, 5, comma, minus, 1, right parenthesis.
Given these coordinates, what is the length of side BCBCB, C of this rectangle?

Answer 1

Answer:

The length of the side BC is 6 units.

Step-by-step explanation:

Distance formula:  

• This works for any two points in 2D space with coordinates (x₁, y₁) for the first point and (x₂, y₂) for the second point
• It is the length of the line segment joining two points

d = $\sqrt{(x_{2} {-} x_{1})^{2} +(y_{2} {-} y_{1})^{2}}$

For the given question:

Rectangle ABCD

Coordinates of Point A,B,C,D

$A = ( 5 , 5)B = (7, 5)C = (7 , -1)D = (5 , -1)$

As we are asked to find the length of side BC, we'll apply the Distance formula on side BC

BC = $\sqrt{(7_ {-} 7)^{2} +(-1 {-} 5)^{2}}$

     = $\sqrt{(0)^{2} +(-6)^{2}}$

     = $\sqrt{ 36}$

     = $6$

Hence, the length of the line side BC is 6.

Learn more about the distance formula here; https://brainly.in/question/49068974

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