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3 years ago

If it is a triangle then it has 4 sides

Mathematics

2 answers:

MArishka [77]3 years ago

4 0

No a triangle has 3 sides. The most common 4 sided figure is a square or rectangle

belka [17]3 years ago

4 0

So a quadrilateral is a four-sided polygon. Since it is a polygon, you know that it is a two-dimensional figure made up of straight sides. A quadrilateral also has four angles formed by its four sides.

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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

gizmo_the_mogwai [7]

Answer:

1) The slope of the line segment AB is $\frac{4}{3}$ .

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

3) The coordinates of the midpoint of the line segment AB is $M(x,y) = (5,7)$ .

4) The slope of a line perpendicular to line segment AB is $-\frac{3}{4}$ .

Step-by-step explanation:

1) Let $A(x,y) = (2,3)$ and $B(x,y) = (8,11)$ . From Analytical Geometry, we get that slope of AB ( $m_{AB}$ ), dimensionless, is determined by the following formula:

$m_{AB} = \frac{y_{B}-y_{A}}{x_{B}-x_{A}}$ (1)

If we know that $x_{A} = 2$ , $x_{B} = 8$ , $y_{A} = 3$ and $y_{B} = 11$ , the slope of the line segment is:

$m_{AB} = \frac{11-3}{8-2}$

$m_{AB} = \frac{4}{3}$

The slope of the line segment AB is $\frac{4}{3}$ .

2) The length of the line segment AB ( $l_{AB}$ ), dimensionless, can be calculated by the Pythagorean Theorem:

$l_{AB} =\sqrt{(x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2}}$ (2)

If we know that $x_{A} = 2$ , $x_{B} = 8$ , $y_{A} = 3$ and $y_{B} = 11$ , the length of the line segment AB is:

$l_{AB} = \sqrt{(8-2)^{2}+(11-3)^{2}}$

$l_{AB} = 10$

The length of the line segment AB is 10.

3) The coordinates of the midpoint of the line segment AB are, respectively:

$x_{M} = \frac{x_{A}+x_{B}}{2}$ (3)

$y_{M} = \frac{y_{A}+y_{B}}{2}$ (4)

If we know that $x_{A} = 2$ , $x_{B} = 8$ , $y_{A} = 3$ and $y_{B} = 11$ , the coordinates of the midpoint of the line segment AB are, respectively:

$x_{M} = \frac{2+8}{2}$

$x_{M} = 5$

$y_{M} = \frac{3+11}{2}$

$y_{M} = 7$

The coordinates of the midpoint of the line segment AB is $M(x,y) = (5,7)$ .

4) From Analytical Geometry we can determine the slope of a line perpendicular to line segment AB as a function of the slope of the line segment:

$m_{\perp} = -\frac{1}{m_{AB}}$ (5)

If we know that $m_{AB} = \frac{4}{3}$ , then the slope of a line perpendicular to AB is:

$m_{\perp} = - \frac{1}{\frac{4}{3} }$

$m_{\perp} = -\frac{3}{4}$

The slope of a line perpendicular to line segment AB is $-\frac{3}{4}$ .

7 0

3 years ago

Anyone would like to do a padlet

denis23 [38]

Answer:

I have my own padlet so sure why not :)

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Marta is solving the equation S = 2πrh + 2πr2 for h. Which should be the result?

geniusboy [140]

Step-by-step explanation:

$S = 2\pi rh + 2\pi {r}^{2} h \\ \\ \therefore \: S = (2\pi r + 2\pi {r}^{2}) h \\ \\ \therefore \: S = 2\pi r(1 + {r}) h \\ \\ \huge \purple{ \boxed{\therefore \: h = \frac{S}{2\pi r(1 + {r})} }}\\$