Mathematics, 26.06.2019 21:00 emileewhitaker1373

The vertices of a triangle are j(1,1) k(2,4) l(5,3) . find the slopes of the lines connecting the vertices. then determine whether the triangle is a right triangle.

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Answer from: mustafaserang582

The triangle is not a right triangle.

Step-by-step explanation:

The given triangle has vertices J(1,1),K(2,4),L(5,3).

The formula for finding the slope is

$m=\frac{y_2-y_1}{x_2-x_1}$

The slope of JK is

$m_{JK}=\frac{4-1}{2-1}=3$

The slope of JL is

$m_{JL}=\frac{5-1}{3-1}=2$

The slope of KL is

$m_{KL}=\frac{5-4}{3-2}=1$

The products of the slopes of the adjacent sides are

$m_{KL}\times m_{JL}=1\times 2=2$

$m_{KL}\times m_{JK}=1\times 3=3$

$m_{JK}\times m_{JL}=3\times 2=6$

None of the products is , which means that no adjacent sides are perpendicular. Hence the triangle is not a right triangle.

Answer from: fayechadx

Yes, the triangle is a right triangle.

Step-by-step explanation:

Since we know that slope formula of the line connecting two points is: $m=\frac{y_2-y_1}{x_2-x_1}$ , where,

m = Slope of the line.

y_2-y_1 = Difference between y-coordinates of two points.

x_2-x_1 = Difference between corresponding x-coordinates of same two points.

Let us find slope of the line connecting points J(1,1) and K(2,4).

$\text{Slope of the line connecting points J and K}=\frac{4-1}{2-1}$

$\text{Slope of the line connecting points J and K}=\frac{3}{1}=3$

Let us find slope of the line connecting points K(2,4) and L(5,3).

$\text{Slope of the line connecting points K and L}=\frac{3-4}{5-2}$

$\text{Slope of the line connecting points K and L}=\frac{-1}{3}$

Let us find slope of the line connecting points L(5,3) and J(1,1).

$\text{Slope of the line connecting points L and J}=\frac{1-3}{1-5}$

$\text{Slope of the line connecting points L and J}=\frac{-2}{-4}$

$\text{Slope of the line connecting points L and J}=\frac{1}{2}$

Since we know that perpendicular lines intersect at right angles to one another and the slopes of perpendicular lines are opposite reciprocals of each other.

We can see that slope of line connecting points J and K is 3, while slope of the line connecting points K and L is $-\frac{1}{3}$ .

Since $-\frac{1}{3}$ is negative reciprocal of 3, therefore, the triangle is a right triangle.

Answer from: Quest

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.

Answer from: Quest

step-by-step explanation:

to determine whether a given function is even, we simply substitute x with -x in the expression. if the result after simplification is identical to the original equation, then the function is said to be even other wise odd.

f(-x) = (-x)^2 - (-x) + 8

= x^2 + x +8

the resulting function is not identical to the original one;

f(-x) ≠ f(x)

therefore, f(x) is not an even function