Rectangle tuvw is on a coordinate plane at t (a, b), u (a + 2, b + 2), v (a + 5, b − 1), and w (a + 3, b − 3). what is the slope of the line that is parallel to the line that contains side tu?

m=1.

Step-by-step explanation:

Rectangle TUVW is on a coordinate plane at T (a, b), U (a + 2, b + 2), V (a + 5, b − 1), and W (a + 3, b − 3). What is the slope of the line that is parallel to the line that contains side TU?

In the coordinate plane, the gradient of a line is to be calculated by using two given points in the plane. Parallel lines are the straight lines that never meet. This is only possible when the gradients of both the lines are same. This means that the slopes of all the parallel lines in a group can be calculated by calculating the slope of one of the lines. Therefore, the slope of the line that is parallel to the line that contains side TU is the same. The point T is (x1, y1)=(a, b) and point U is (x2, y2)=(a+2, b+2). The formula of the gradient is:

m = (y2 - y1)/(x2 - x1).

m = (b+2 - b)/(a+2 - a).

a and b cancel out so:

m = 2/2 = 1.

The slope of the line that is parallel to the line containing the side TU is 1!!!

The slope of the line which is parallel to the line that contains side TU is 1.

Even though we are given information about the whole rectangle, to solve this problem we only need the given information about points T and U. The geometrical definition of parallel lines are lines which, when graphed on a 2D plane, never cross. In mathematical terms, this means that any pair of parallel lines share the same slope.

The slope of a curve (or in this case a line) is the ratio of how much does that curve rise (or fall) when we move along it over a certain horizontal distance. A typical definition of the slope is the "rise over run" definition.

Therefor, the answer to this problem will be any line that has the same slope as that of side TU. Having the coordinates of points T and U, we can find the slope of their line by using the following formula:

It is to be noted that even when 2 lines are the same (meaning that they intersect infinitely at every point, they are also considered to be parallel (because they share the same slope).

Slope, parallel, rectangle.