shriyasoni150

23.06.2019 •

Mathematics

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Ответ:

IntellTanito

28.08.2020

Mathematics

Part A:

The length of segment DE is √(17)

The length of segment DF is √(17)

The length of segment EF is 3·√2

Part B:

The slope of segment DE is 4

The slope of segment DF is 1/4

The slope of segment EF is -1

Part C:

The triangle is an isosceles triangle

Step-by-step explanation:

Part A:

The vertices of the triangle ΔDEF are given as follows;

D(2, 1), E(3, 5), and F(6, 2)

The equation for the length of a segment, l, is given as follows;

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

The length of segment DE is $l_{DE} = \sqrt{\left (5-1 \right )^{2}+\left (3-2 \right )^{2}} = \sqrt{17}$

The length of segment DF is $l_{DF} = \sqrt{\left (2-1 \right )^{2}+\left (6-2 \right )^{2}} = \sqrt{17}$

The length of segment EF is $l_{EF} = \sqrt{\left (2-5 \right )^{2}+\left (6-3 \right )^{2}} = 3 \cdot \sqrt{2}$

Part B:

The slope of a segment, m, is given by the following relation;

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

The slope of segment DE is given as follows;

$m =\dfrac{5-1}{3-2} = 4$

The slope of segment DF is given as follows;

$m =\dfrac{2-1}{6-2} = 1/4$

The slope of segment EF is given as follows;

$m =\dfrac{2-5}{6-3} = -1$

Part C:

The triangle is an isosceles triangle because it has two sides that are equal.

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