Question

Find the perimeter of the rectangle whose vertices are the points that coordinates (1,-4)(7,-4)(1,7)(7,7)

Answer 1

34 units

Explanation:

A line connecting two points is known as a line segment.

Following are the four points (or vertices) of the rectangle:

A (1, -4)

B (7, -4)

C (1, 7)

D (7, 7)

When these vertices are to plotted on a graph paper, it will be observed that line segments AB and CD are horizontal lines (which are parallel to each other and equal in measurement) and line segments AC and BD are vertical lines (which are parallel to each other and equal in measurement)

Length of a horizontal line = Difference in x-coordinates

Length of a vertical line = Difference in y-coordinates

Line segment AB = Line segment CD = Width of rectangle = w

Line segment AC = Line segment BD = Length of rectangle = l

l =
`[7 - (-4)]` units

=
`(7 + 4)` units

= 11 units

w =
`(7 - 1)` units

= 6 units

Perimeter of rectangle =
`2 [l + w]` units

=
`2 [11 + 6]` units

=
`2(17)` units

= 34 units