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2 years ago

Determine the value of X AB is the mid segment of triangle LMN. Determine the value of X

Mathematics

1 answer:

r-ruslan [8.4K]2 years ago

7 0

Answer:

Step-by-step explanation:

Since ,AB is the mid segment of triangle LMN

Then

$\Longleftrightarrow AB=\frac{MN}{2}$

$\Longleftrightarrow x+8=\frac{5x+4}{2}$

$\Longleftrightarrow 2\times(x+8)=5x+4$

$\Longleftrightarrow 2x+16=5x+4$

$\Longleftrightarrow 16-4=5x-2x$

$\Longleftrightarrow 3x=12$

$\Longleftrightarrow x=\frac{12}{3}=4$

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Below represents the proof that the quadrilateral QRST is a parallelogram

<h3>How to prove that QRST is a parallelogram?</h3>

The coordinates are given as:

Q = (-1,-1)

R = (2,9)

S = (-4,5)

T = (-7,-5)

Calculate the length of each side using:

$d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}$

So, we have:

$QR = \sqrt{(-1 - 2)^2 + (-1 -9)^2} = \sqrt{109}$

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The above computations show that opposite sides are equal.

Next, we determine the slope of each side using:

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

So, we have:

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$RS = \frac{5-9}{-4 - 2} = \frac{2}3$

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$TQ = \frac{-5+1}{-7 + 1} = \frac{2}3$

The above computations show that opposite sides are parallel, because they have equal slope

Hence, the quadrilateral QRST is a parallelogram