Question

Consider a rectangle, where two adjacent vertices of a rectangle are located at the coordinates (-3 , 1) and (5 , 1). Two sides of this rectangle have a length of 6 units. Possible coordinates for one of the two missing vertices is ? The length of the diagonal of the rectangle is ? units.

Answer 1

To find the missing vertices, use the fact that opposite sides of a rectangle are equal. The missing vertices are (-3, 7) and (5, 7). To find the length of the diagonal, use the distance formula. The length of the diagonal is 10 units.

Step-by-step explanation:

To find the missing vertices, we can use the fact that opposite sides of a rectangle are equal in length. Since two sides of the rectangle have lengths of 6 units, the other two sides must also have lengths of 6 units. Therefore, the missing vertices can be located at (-3, 7) and (5, 7).

To find the length of the diagonal of the rectangle, we can use the distance formula. The formula is sqrt((x2 - x1)^2 + (y2 - y1)^2). Plugging in the coordinates (-3, 1) and (5, 7) into the formula, we get sqrt((5 - (-3))^2 + (7 - 1)^2) = sqrt(64 + 36) = sqrt(100) = 10 units. Therefore, the length of the diagonal of the rectangle is 10 units.

Answer 2

co-ordinates are (-3,7) and (5,7)

or

(-3,-5) and (5,-5)

length of diagonal=10 units

Step-by-step explanation:

`length=√((5+3)^2+(1-1)^2) =√(64) =8\\slope ~of~length=(1-1)/(5+3) =0\\\\length ~of~rectangle~is~parallel~to~x-axis\\ width~ is~ parallel ~to~y- axis~and~is~6~units~away~from~length.\\other co-ordinates ~of~rectangle are~(-3,1+6)~and ~(5,1+6)~or~(-3,7)~and~(5,7)\\and~other~co-ordinates~are~(-3,1-6)~and~(5,1-6)~or~(-3,-5)~and~(5,-5)`

length of diagonal

d=\sqrt{8^2+6^2} =\sqrt{64+36} =\sqrt{100} =10 ~units\\or\\d=\sqrt{(5+3)^2+(1-7)^2} =\sqrt{64+36} =\sqrt{100} =10~units.