What is the area of the composite figure whose vertices have the following coordinates?
2 answers:
Answer:
24
Step-by-step explanation:
From the picture you can see that area is sume of area P1 and area P2.
a=6 because its egdes are on point -2 and 4, so it is 6. (See x-ose)
h=3 Edges on -2 and 1 (see y-ose)
k=2 edges on 3 and 1 on y-ose
P1=a*h=6*3=18
P2=a*k/2=6*2/2=6
P=18+6=24
Answer:
24 square units
Step-by-step explanation:
The area of a polygon can be computed from its list of coordinates as ...
where there are n coordinate points. Subscripts on y "wrap around" so that ...
The area from these coordinates is ...
A = (1/2)|-2(-2-1) +4(1-(-2)) +5(3-(-2)) +2(1-1) -1(-2-3)|
= (1/2)|6 +12 +25 +0 +5|
= (1/2)(48)
= 24 . . . . square units
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If you graph the points, you see that the figure can be considered to be a parallelogram topped by a triangle. The area of the parallelogram is ...
A = bh = 6·3 = 18
The area of the triangle is ...
A = 1/2bh = (1/2)(6)(2) = 6
Then the total area is 18+6 = 24, which agrees with the above calculation.
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Answer:
3. ∠BDE ≅ ∠BAC; Corresponding Angles Postulate 5. ΔBDE ~ ΔBAC; Angle-Angle (AA) Similarity Postulate
Step-by-step explanation:
3) Statement ∠BDE ≅ ∠BAC;
Corresponding Angles Postulate
The Corresponding Angles Postulate states that given two parallel lines, in this case DE and AC cut by a transversal one (AB) than these corresponding angles are congruent.
5) ΔBDE ~ ΔBAC; Angle-Angle (AA) Similarity Postulate
If two pairs of corresponding angles are congruent (∠D and ∠A, ∠E and ∠C) than these triangles are similar.
Answer:
(x, y) = (1, 3)
Step-by-step explanation:
The "work" of solving by graphing is typing the equations into a graphing calculator and highlighting the point of intersection.
___
If you're graphing these by hand, there are a couple of strategies you can use. One is to make use of the intercepts of the line. For each of these, you need to rearrange the equation to a suitable form.
<u>3y -6 = 3x</u>
To put this into "intercept form", put the variable terms on one side of the equal sign and the constant on the other. Then divide by the constant and express the resulting variable coefficients as denominators.
3x -3y = -6
x/(-6/3) +y/(-6/-3) = 1
x/(-2) + y/2 = 1 . . . . . . The x-intercept is -2; the y-intercept is 2.
Plot the intercept points and draw a line through them.
<u>y +2x = 5</u>
The intercepts for this one are found by dividing by 5:
x/(5/2) + y/5 = 1 . . . . . . The x-intercept is 2.5; the y-intercept is 5.
The other strategy you can use for this one is to rearrange the equation to slope-intercept form and make use of those numbers.
y = -2x + 5
The y-intercept is 5 (as we already found above), and the slope is -2. That means the line drops 2 units for each unit it goes to the right. Apart from the y-intercept, other points on this line will be (1, 3), (2, 1), (3, -1).
<u>Solution</u>
When you plot these lines, you find they intersect at (1, 3). That is the solution to the system of equations, the values of x and y that satisfy both equations.
Hope this helps! Don’t mind the part I crossed off.
