Mathematics, 01.12.2020 18:20 aaliyahbaladez56

A line segment AB has the coordinates A (2,3) AND B ( 8,11) answer the following questions (1) What is the slope of AB? (2) What is the length of AB? (3) What are the coordinates of the mid point of AB?(4) What is the slope of a line perpendicular to AB ?

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Answer from: terrellsmith84

(1) The slope of the line segment AB is 1. $\bar 3$

(2) The length of the line segment AB is 10

(3) The coordinates of the midpoint of AB is (5, 7)

(4) The slope of a line perpendicular to the line AB is-0.75

Step-by-step explanation:

The coordinates of the line segment AB are;

A(2, 3) and B(8, 11)

(1) The slope of a line segment is given by the following equation;

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Where;

(x₁, y₁) and (x₂, y₂) are two points on the line segment

Therefore;

The slope, m, of the line segment AB is given as follows;

A(2, 3) = (x₁, y₁) and B(8, 11) = (x₂, y₂)

$Slope, \, m_{AB} =\dfrac{11-3}{8-2} = \dfrac{8}{6} = 1 \frac{1}{3} = 1.\bar3$

The slope of the line segment AB = 1. $\bar 3$

(2) The length, l, of the line segment AB is given by the following equation;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

Therefore, we have;

$l_{AB} = \sqrt{\left (11-3 \right )^{2}+\left (8-2 \right )^{2}} = \sqrt{64 +36} = 10$

The length of the line segment AB is 10

(3) The coordinates of the midpoint of AB is given as follows;

$Midpoint, M = \left (\dfrac{x_1 + x_2}{2} , \ \dfrac{y_1 + y_2}{2} \right )$

Therefore;

$Midpoint, M_{AB} = \left (\dfrac{2 + 8}{2} , \ \dfrac{3 + 11}{2} \right ) = (5, \ 7)$

The coordinates of the midpoint of AB is (5, 7)

(4) The relationship between the slope, m₁, of a line AB perpendicular to another line DE with slope m₂, is given as follows;

$m_1 = -\dfrac{1}{m_2}$

Therefore, the slope, m₁, of the line perpendicular to the line AB, that has a slope m₂ = 4/3 = 1. $\bar 3$ is given as follows;

$m_1 = -\left (\dfrac{1}{\frac{4}{3} } \right ) = -\dfrac{3}{4} = -0.75$

The slope, m₁, of the line perpendicular to the line AB is m₁ = -0.75.

Answer from: Quest

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

Answer from: Quest

y-y1=4(x-x1)

step-by-step explanation:

this is point-slope form since you only have 4 as the slope it goes in place of m

hope this : )

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A line segment AB has the coordinates A (2,3) AND B ( 8,11) answer the following questions (1) What...

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