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3 years ago

13

Which sentence fully illustrates that polygon ABCD is congruent to polygon PQRS?

1 answer:

fredd [130]3 years ago

8 0

"This symbol indicates that two objects are congruent: ≅. Congruent means that the two polygons are exactly the same in every way. They have the same number of sides and angles. Their angles are congruent. When two polygons are congruent, they can be placed on top of one another and will match exactly. Congruent polygons may sometimes be turned, or rotated, but they are still congruent if you can place one polygon on top of the other and create an exact match.Therefore, the sentence ABCD ≅ PQRS illustrates that these two polygons are congruent."

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frosja888 [35]

Complete Question:

The given line segment has a midpoint at (3, 1). On a coordinate plane, a line goes through (2, 4), (3, 1), and (4, -2).

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Answer:

$y = \frac{1}{3}x$

Step-by-step explanation:

From the question, we understand that the line goes through $(2, 4), (3, 1), and\ (4, -2).$

First, we calculate the slope of the above points

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

Where

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$(x_2,y_2) = (3,1)$

$m = \frac{1 - 4}{3 - 2}$

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Also; from the question, we understand that the line segment is perpendicular to the above points.

This slope (m2) of the line segment is calculated as:

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$m_2 = \frac{1}{3}$

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$y - y_1 = m_2(x - x_1)$

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So:

$y - 1 = \frac{1}{3}(x - 3)$

Open bracket

$y - 1 = \frac{1}{3}x - 1$

Add 1 to both sides

$y - 1 +1= \frac{1}{3}x - 1+1$

$y = \frac{1}{3}x$

Hence, the equation of the line segment is: $y = \frac{1}{3}x$

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