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3 years ago

6

A triangle has vertices at S(1,1),T(2,-3), and U(4,0). The triangle is translated up 3 units. What are the coordinates of the ve

rtices of the image?

1 answer:

Luba_88 [7]3 years ago

7 0

S(1,4), T(2,0), U(4,3)

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Drag and drop a statement or reason to each box to complete the proof.

zhannawk [14.2K]

The data observed from the triangle are given below.

Statement Reason

$\overline{P Q} \cong \overline{P R}$ Given

Draw $\overline{P M}$ so that M is the midpoint of QR. Two points determine a line

$\overline{Q M} \cong \overline{R M}$ Definition of midpoint

$\overline{P M} \cong \overline{P M}$ Reflexive property of congruence

$\triangle P Q M \cong \Delta P R M$ SSS congruence postulate

$\angle \mathrm{Q} \cong \angle \mathrm{R}$ CPCTC

SSS means side-side-side

CPCTC means corresponding parts of the congruence triangle are congruent.

Hence the given triangle is SSS congruence postulate

8 0

3 years ago

A gardener has 3 pounds of compost. She will split the compost into 8 garden beds equally. How many pounds of compost will she p

Korolek [52]

Answer:

3/8 pounds of compost

Step-by-step explanation:

Find how much compost she'll put in each garden bed by dividing the number of pounds of compost by the number of garden beds:

3/8

This fraction cannot be simplified further, so the answer is 3/8.

She will put 3/8 pounds of compost into each garden bed

6 0

3 years ago

Solve the system y = -x + 7 and y = -0.5(x - 3)2 + 8

guajiro [1.7K]

I believe the answer is (7,0) and (1,6). I hope it's correct :)

6 0

3 years ago

Read 2 more answers

Find the value of x in the triangle.

Musya8 [376]

The answer is 38 degrees because for every triangle, the angles add up to 180 and the small square on the triangle represents it is a right triangle, which has 90 degrees. 38 + 52 + 90 = 180

6 0

3 years ago

Find the area of the given triangle to the nearest square unit. Angle a= 30 degrees, b=10, angle B=45 degrees

storchak [24]

Answer:

$A=34\ units^2$

Step-by-step explanation:

Suppose we have a general triangle like the one shown in the figure.

We know the angle A, the angle B and the length b.

$A = 30\°\\\\B = 45\°\\\\b = 10$

By definition I know that the sum of the internal angles of a triangle is always equal to 180 °.

So

$A + B + C = 180\\\\30 + 45 + C = 180$

We solve the equation and thus we find the angle C.

$C = 180 - 30-45\\\\C = 105$

We already know the three triangle angles.

Now we use the sine theorem to calculate the sides c and a.

The sine theorem says that:

$\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}$

Then

$\frac{sin(30)}{a}=\frac{sin(45)}{10}$

$\frac{sin(30)}{\frac{sin(45)}{10}}=a$

$a=7.071$

Also

$\frac{sin(105)}{c}=\frac{sin(45)}{10}$

$\frac{sin(105)}{\frac{sin(45)}{10}}=c$

$c=13.660$

Finally, we use the Heron formula to calculate the triangle area

$A=\sqrt{s(s-a)(s-b)(s-c)}$

Where s is:

$s=\frac{a+b+c}{2}$

Therefore

$s=\frac{7.071+10+13.660}{2}$

$s=15.37$

$A=\sqrt{15.37(15.37-7.071)(15.37-10)(15.37-13.66)}$

$A=34\ units^2$

3 0

3 years ago