Answer:
C. [tex]3\sqrt{5}[/tex] units
Step-by-step explanation:
To find the length of the diagonal from vertex J to vertex L in the quadrilateral J(1,6) L(7,3), we can use the distance formula in coordinate geometry.
The distance formula between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] in a coordinate plane is given by:
[tex]\textsf{Distance (d)}= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
For the points [tex]J(1,6)[/tex] and [tex]L(7,3)[/tex], we can calculate the distance as follows:
[tex]\textsf{d}_\textsf{JL}= \sqrt{(7 - 1)^2 + (3 - 6)^2} [/tex]
[tex]\textsf{d}_\textsf{JL}= \sqrt{(6)^2 + (-3)^2} [/tex]
[tex]\textsf{d}_\textsf{JL}= \sqrt{36 + 9} [/tex]
[tex]\textsf{d}_\textsf{JL}= \sqrt{45} [/tex]
[tex]\textsf{d}_\textsf{JL}= 3\sqrt{5} [/tex]
So, the length of the diagonal from vertex J to vertex L is:
C. [tex]3\sqrt{5}[/tex] units
