Triangle PQR is transformed to the similar triangle P′Q′R′.
A coordinate grid is shown from negative 10 to 0 to positive 10 on both x- and y-axes at increments of 1. A triangle PQR has P at ordered pair 4, negative 4, Q at 8, negative 4, R at 4 and negative 8. A polygon P prime Q prime R prime has P prime at ordered pair 2, negative 2, Q prime at ordered pair 4, negative 2, R prime at ordered pair 2, negative 4.
What is the scale factor of dilation? (1 point)
1 over 2
1 over 3
1 over 4
1 over 5
To find the scale factor of the dilation, we can compare the corresponding side lengths between the two triangles.
The length of side PQ in triangle PQR is 8 - 4 = 4 units.
The length of side P'Q' in triangle P'Q'R' is 4 - 2 = 2 units.
The scale factor can be found by taking the ratio of these side lengths:
Scale factor = Length of P'Q' / Length of PQ = 2/4 = 1/2.
Therefore, the scale factor of dilation is 1/2.
Two similar polygons are shown below:
A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A polygon PQRS is shown with vertex P on ordered pair negative 4, negative 2, vertex Q on ordered pair negative 4, negative 6, vertex R on ordered pair negative 2, negative 4 and vertex S on ordered pair negative 2, negative 2. A polygon P prime Q prime R prime S prime is shown with vertex P prime on ordered pair negative 2, negative 1, vertex Q prime on ordered pair negative 2 , negative 3, vertex R prime on ordered pair negative 1, negative 2 and vertex S prime on ordered pair negative 1, negative 1.
Which transformation was performed on PQRS to form P′Q′R′S′? (1 point)
A dilation factor of 2
A dilation factor of 4
A dilation factor of 1 over 2
A dilation factor of 1 over 4
To determine the transformation performed on the polygon PQRS to form P'Q'R'S', we can compare the corresponding side lengths between the two polygons.
The length of side PQ in polygon PQRS is 2 - 6 = 4 units.
The length of side P'Q' in polygon P'Q'R'S' is -3 - (-6) = 3 units.
The length of side PS in polygon PQRS is (-2) - (-2) = 0 units.
The length of side P'S' in polygon P'Q'R'S' is (-1) - (-1) = 0 units.
The length of side QR in polygon PQRS is (-2) - (-4) = 2 units.
The length of side Q'R' in polygon P'Q'R'S' is (-1) - (-2) = 1 unit.
The length of side RS in polygon PQRS is (-4) - (-2) = -2 units.
The length of side R'S' in polygon P'Q'R'S' is (-2) - (-2) = 0 units.
By comparing the side lengths, we can see that the corresponding sides have been dilated by a factor of 1/2.
Therefore, the transformation performed on PQRS to form P'Q'R'S' is a dilation factor of 1/2.
17.
(02.06 LC)
A pair of parallel lines is cut by a transversal, as shown below:
A pair of parallel lines is cut by a transversal. The exterior angle made on the right by the intersection of the upper parallel line and the transversal is labeled as p. The exterior angle made on the left by the intersection of the lower parallel line and the transversal is labeled as q.
Which of the following best represents the relationship between angles p and q? (1 point)
p = 180° − q
q = 180° − p
p = 2q
p = q
The relationship between angles p and q in this scenario is that p and q are supplementary angles.
Supplementary angles add up to 180 degrees. Therefore, p + q = 180°.
So, the correct answer is:
p = 180° - q.
Which relationship is always correct for the angles x, y, and z of triangle ABC? (1 point)
A triangle ABC has angle ABC labeled as y, angle ACB labeled as z, and the exterior angle at A labeled as x.
x + z = y
y + z = x
x + y + z = 180 degrees
x + y + z = 90 degrees
The correct relationship for the angles x, y, and z of triangle ABC is:
x + y + z = 180 degrees.
This is known as the angle sum property of triangles, which states that the sum of the interior angles of a triangle is always equal to 180 degrees.
What is the length of the unknown side of the right triangle? (1 point)
A right triangle with hypotenuse x and legs 7 and 24
7
24
25
31
To find the length of the unknown side of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the two legs.
In this case, the lengths of the legs are 7 and 24.
Using the Pythagorean theorem:
x^2 = 7^2 + 24^2
x^2 = 49 + 576
x^2 = 625
Taking the square root of both sides:
x = √625
x = 25
Therefore, the length of the unknown side of the right triangle is 25.
The correct answer is:
25
ABCD is a rectangle. What is the value of x? (1 point)
rectangle with length 56 m, width x m, and diagonal 65 m
9 meters
28 meters
33 meters
65 meters