Paulkennethidn
Answered

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the coordinates of the vertices of a rectangle are (-2,6), (10,6), (10,-3), (-2,-3). what is the length of a diagonal of the rectangle?

Sagot :

Without plotting the points on the graph, you can determine which opposite vertices have to be connected to form the diagonals of the rectangle.

Points on opposite quadrants, when connected form the diagonals of the rectangle.
Its diagonals are congruent.

Quadrant I (+,+) and Quadrant III (-,-) are opposites.
Quadrant II (-,+) and Quadrant IV (+,-) are opposites.

Points/Vertices (10, 6) and (-2, -3) are opposites.
Points/Vertices (-2, 6) and ( 10, -3) are opposites.

Solve for the length of a diagonal of the rectangle by using the distance formula:
DISTANCE = [tex] \sqrt{(x _{2} - x_{1}) ^{2}+(y _{2} -y _{1} ) ^{2} } [/tex]

D = [tex] \sqrt{(-2-10) ^{2}+(-3-6) ^{2} } [/tex]

[tex]D = \sqrt{(-12) ^{2} +(-9) ^{2} } [/tex]

[tex]D = \sqrt{144 + 81} [/tex]

[tex]D = 15 units[/tex] [tex]D= \sqrt{225} [/tex]

The length of a diagonal is 15 units.





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