What is the area of this triangle in the coordinate plane? 5 units² 6 units² 7 units² 12 units² A graph with a triangle drawn be
tween coordinates begin ordered pair 1 comma 1 end ordered pair begin ordered pair 1 comma 4 end ordered pair and coordinates begin ordered pair 5 comma 1 end ordered pair
1 answer:
Answer:
6 units²
Step-by-step explanation:
The coordinates (1,1) (1,4) (5,1) form a right triangle as shown in the graph below
The base is is (1,1) and (5,1) so the length is 5-1 or 4 units
The height is (1,1) and (1,4) so the height is 4-1 or 3 units
Area of a triangle is given by
A = 1/2 bh
= 1/2 (4*3)
= 1/2 *12
= 6 units^2
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An equation that can be used to determine the tree's height is 22.5/8.25 = x/5.5.
The height of this tree is equal to 15 feet.
The distance of this person from the tree is equal to 14.25 feet.
<h3>What are the properties of similar triangles?</h3>In Geometry, two (2) triangles are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.
Additionally, two (2) geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.
Now, we can write an equation that can be used to determine the tree's height. Since the ratio of the corresponding sides of similar triangles are equal in magnitude, we have the following mathematical expression (equation):
22.5/8.25 = x/5.5
Where:
x represents the height of the tree.
<h3>How tall is the tree?</h3>22.5/8.25 = x/5.5
Cross-multiplying, we have:
8.25x = 22.5 × 5.5
8.25x = 123.75
x = 123.75/8.25
x = 15 feet.
<h3>How far is the person standing from the tree?</h3>The distance of this person from the tree can be calculated as follows;
Distance = Length of tree's shadow - Length of person's shadow
Distance = 22.5 - 8.25
Distance = 14.25 feet.
Read more on corresponding side here: brainly.com/question/11920446
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