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4 years ago

Find the value of x 46. 92. 78. 98.

Mathematics

1 answer:

Aloiza [94]4 years ago

8 0

Answer:

x = 92

Step-by-step explanation:

The segment of measure 46 joins the midpoints of 2 sides of the triangle and is one half the measure of the third side, thus

x = 2 × 46 = 92

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3 years ago

Determine whether a figure with the given vertices is a rectangle using the Distance Formula.

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Answer:

Yes; Opposite sides are congruent, and diagonals are congruent.

Step-by-step explanation:

we have

$A(4, -7), B(4, -2), C(0, -2), D(0, -7)$

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the length of the sides

Find the distance AB

substitute the values

$d=\sqrt{(-2+7)^{2}+(4-4)^{2}}$

$d=\sqrt{(5)^{2}+(0)^{2}}$

$AB=5\ units$

Find the distance BC

substitute the values

$d=\sqrt{(-2+2)^{2}+(0-4)^{2}}$

$d=\sqrt{(0)^{2}+(-4)^{2}}$

$BC=4\ units$

Find the distance CD

substitute the values

$d=\sqrt{(-7+2)^{2}+(0-0)^{2}}$

$d=\sqrt{(-5)^{2}+(0)^{2}}$

$CD=5\ units$

Find the distance AD

substitute the values

$d=\sqrt{(-7+7)^{2}+(0-4)^{2}}$

$d=\sqrt{(0)^{2}+(-4)^{2}}$

$AD=4\ units$

Compare the length sides

AB=CD

BC=AD

therefore

Opposite sides are congruent

step 2

Find the length of the diagonals

Find the distance AC

substitute the values

$d=\sqrt{(-2+7)^{2}+(0-4)^{2}}$

$d=\sqrt{(5)^{2}+(-4)^{2}}$

$AC=\sqrt{41}\ units$

Find the distance BD

substitute the values

$d=\sqrt{(-7+2)^{2}+(0-4)^{2}}$

$d=\sqrt{(-5)^{2}+(-4)^{2}}$

$BD=\sqrt{41}\ units$

Compare the length of the diagonals

AC=BD

therefore

Diagonals are congruent

The figure is a rectangle, because Opposite sides are congruent, and diagonals are congruent

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