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Find the length and width op the quadrilateral with vertices at
(6,4),(4,4,(6,7),(4,7).

Find the length and width op the quadrilateral with vertices at $(6,4),(4,4,(6,7),(4,7)$ .

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Find the magnitude of a three-dimensional vector

Full solution

Q. Find the length and width op the quadrilateral with vertices at

(6,4),(4,4,(6,7),(4,7)

.

Identify Coordinates and Plot: Identify the coordinates of the vertices of the quadrilateral and plot them if necessary to understand the shape. $\newline$ Vertices: $A(6,4)$ , $B(4,4)$ , $C(6,7)$ , $D(4,7)$ . $\newline$ By looking at the coordinates, we can see that $AB$ and $CD$ are horizontal lines, and $AD$ and $BC$ are vertical lines. This suggests that the quadrilateral is a rectangle.
Calculate Length of AB: Calculate the length of AB. Length $AB = x$ -coordinate of $B - x$ -coordinate of $A = 4 - 6 = -2$ . Since length cannot be negative, we take the absolute value. Length $AB = |-2| = 2$ .
Calculate Length of AD: Calculate the length of AD. $\newline$ Length $AD = y$ -coordinate of $D - y$ -coordinate of $A = 7 - 4 = 3$ .
Confirm Rectangle Shape: Since $AB$ and $CD$ are parallel and equal in length, and $AD$ and $BC$ are parallel and equal in length, and all angles are right angles, we confirm that the quadrilateral is a rectangle. $\newline$ Therefore, the length of the rectangle is the longer side, and the width is the shorter side.
Determine Length and Width: Determine which side is the length and which is the width. $\newline$ Since $AB = 2$ and $AD = 3$ , the length of the rectangle is $3$ and the width is $2$ .

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