# Is on a at t (a, b), u (a + 2, b + 2), v (a + 5, b ? 1), w (a + 3, b ? 3). is ofis touv?

m = -1 (Option C)

Step-by-step explanation:

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 UV is the same. The point U is (x1, y1)=(a+2, b+2) and point V is (x2, y2)=(a+5, b-1). The formula of the gradient is:

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

m = (b-1 - (b+2))/(a+5 - (a+2)).

m = (b-1 - b-2))/(a+5 - a-2).

a and b cancel out so:

m = -3/3 = -1.

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

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 correct option is;

A 1

Step-by-step explanation:

The given rectangle TUVW has coordinates T(a, b), U (a + 2, b + 2), V ( a + 5, b - 1) and W (a + 3, b - 3).

Given that the coordinates of T and U are T (a, b), and U (a + 2, b + 2), we have;

The slope, m of the line TU is is found by the following relation;

Where we put (x₁, y₁) = (a, b) and (x₂, y₂) = (a + 2, b + 2), we have;

m = ((b + 2) - b)/((a + 2) - a) = 2/2 = 1

Whereby the slope of a line parallel to another line are equal, we have that the slope of the line parallel to the line that contains the side TU is also 1.

The slope of the line is 1

Step-by-step explanation:

* Lets revise how to find a slope of a line and what is the relation

between the slopes of the parallel lines

- The slope of the line whose endpoints are (x1 , y1) and (x2 , y2) is

- The parallel lines have same slopes

* Lets solve the problem

- TUVW is a rectangle

- T = (a , b) , U = (a + 2 , b + 2) , V = (a + 5 , b + 1) , W = (a + 3 , b + 3)

- Lets find the slope of line TU

∵ T = (a , b) and U = (a + 2 , b + 2)

- Let T is (x1 , y1) and U is (x2 , y2)

∵ x1 = a , x2 = a + 2

∵ y1 = b , y2 = b + 2

∴ The slope of TU

- The slope of the line that contain the side TU equal the slope of the

side TU

∴ The slope of the line contains side TU is 1

∵ The parallel lines have same slopes

∴ The slope of the line that is parallel to the line that contains side

TU equal the slope of the line contains side Tu

∵ The slope of the line contains side TU is 1

∴ The slope of the line is 1

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

Further explanationEven 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).

Learn moreSlope of a line: Undefined slope of a line: KeywordsSlope, parallel, rectangle.

Explanation:

W = (a+3, b-3)

V = (a+5, b-1)

Let (x1,y1) = (a+3, b-3) and (x2,y2) = (a+5, b-1)

Compute the slope using the slope formula

m = slope

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

m = ( (b-1) - (b-3) )/( (a+5) - (a+3) )

m = (b-1 - b+3)/(a+5 -a-3)

m = 2/2

m = 1

Conveniently all the variable terms (of 'a's and 'b's) cancel out leaving us with a single number. It doesn't matter what the value of 'a' or 'b' is, as the slope of WV is always 1.

The slope of any parallel line to WV will also be 1 as well. Parallel lines have equal slopes, but different y intercepts.