Answer:
A. △ABC ~ △DEC
B. ∠B ≅ ∠E
D. 3DE = 2AB
Step-by-step explanation:
Transformation involves the reshaping or resizing of a given figure. The types are: reflection, dilation, rotation and translation.
In the given question, the two operations performed on triangle ABC are reflection and dilation to form triangle DEC. The length of each side of triangle DEC is two-third of that of ABC. Therefore, the correct statements about the two triangles are:
i. △ABC ~ △DEC
ii. ∠B ≅ ∠E
iii. 3DE = 2AB
<u>Answer:</u>
The correct answer option is D.
.
<u>Step-by-step explanation:</u>
We are to find the equation of a line which is perpendicular to the following line and passes through the point (3, 4):

We know that an equation perpendicular to another equation has a slope which is the negative reciprocal of the first equation.
So our required slope is 
Finding the y-intercept:



Therefore, the equation of the line perpendicular to
and passing through the point (3, 4) is
.
Answer:
3/4
Step-by-step explanation:
18:24=18/24
18/24 reduces to 3/4
Let's find the area of the base.
It's a rectangle that's 3.8 by 4.8, so let's multiply.
3.8×4.8=18.24
We have two different triangles.
Triangle one has a height of 2.6 and base of 4.8. But there are two of them.
2.6×4.8×0.5=6.24×2= 12.48; this is the area of two triangles.
Another set of triangles has a height of 2.9 and a base of 3.8.
2.9×3.8×0.5=5.51×2=11.02
Let's add all the areas together.
18.24+12.48+11.02
41.74
The surface area is 41.74 m², so the third option.
Answer:
(D)The midpoint of both diagonals is (4 and one-half, 5 and one-half), the slope of RP is 7, and the slope of SQ is Negative one-sevenths.
Step-by-step explanation:
- Point P is at (4, 2),
- Point Q is at (8, 5),
- Point R is at (5, 9), and
- Point S is at (1, 6)
Midpoint of SQ 
Midpoint of PR 
Now, we have established that the midpoints (point of bisection) are at the same point.
Two lines are perpendicular if the slope of one is the negative reciprocal of the other.
In option D
- Slope of SQ

Therefore, lines RP and SQ are perpendicular.
Option D is the correct option.