Find the midpoint of line segment AB whose endpoints are A(2,−3) and B(−4,6).
(-1, 1.5).
100
Line segment AB is tangent to circle O at A. Which type of triangle is always formed when points A, B, and O are connected?
right triangle
100
The degree measures of the angles of triangle ABC are represented by x, 3x, and 5x - 54. Find the value of x.
x = 26
100
The measures of two consecutive angles of a parallelogram are in the ratio 5:4. What is the measure of an obtuse angle of the parallelogram?
100 degrees
100
Towns A and B are 16 miles apart. How many points are 10 miles from town A and 12 miles from town B?
2 points
200
In circle O, diameter RS has endpoints R(3a,2b − 1) and
S(a − 6,4b + 5). Find the coordinates of point O, in terms of a and b. Express your answer in simplest form.
O (2a-3, 3b+2)
200
How many common tangent lines can be drawn to the two externally tangent circles?
3
200
The angles of triangle ABC are in the ratio of 8:3:4. What is the measure of the smallest angle?
36 degrees
200
Identify the quadrilateral(s) that have perpendicular diagonals.
Rhombus and Square
200
What is the total number of points equidistant from two intersecting straight roads and also 300 feet from the traffic light at the center of the intersection?
4 points
300
Find the length of a line segment whose endpoints are (4,7) and (1,11).
distance = 5 units
300
If a diameter is drawn perpendicular to a chord, what happens to the chord?
It is bisected.
300
In triangle FGH , m∠F = 42 and an exterior angle at vertex H has a measure of 104. What is m∠G?
< G = 62 degrees
300
In isosceles trapezoid ABCD, AB ≅ CD. If BC = 20, AD = 36, and AB = 17, what is the length of the altitude of the trapezoid?
15
300
Point P is located on AB. Draw and describe the locus of points that are 3 units from AB and 5 units from point P.
Correct diagram is drawn. 2 lines parallel to AB and 3 units away. A circle with a radius of 5 and P as the center.
400
Tangents PA and PB are drawn to circle O from an
external point, P, and radii OA and OB are drawn.
If m∠APB = 40, what is the measure of ∠AOB?
140 degrees
400
In a circle, an inscribed angle intercepts an arc whose measure is (14x − 2)°. Express, in terms of x, the number of degrees in the measure of the inscribed angle.
7x - 1 degrees
400
A box contains one 2-inch rod, one 3-inch rod, one 4-inch rod, and one 5-inch rod. What is the maximum number of different triangles that can be made using these rods as sides?
3 triangles
400
The coordinates of quadrilateral PRAT are P(a,b), R(a,b + 3), A(a + 3,b + 4), and T(a + 6,b + 2).
Prove that RA is parallel to PT.
RA is parallel to PT because they have the same slope of 1/3.
400
In a coordinate plane, how many points are both 5 units from the origin and 2 units from the x-axis? State the equations of each locus.
4 points. A circle whose center is (0,0) and radius is 5.
x2 + y2 =25
y = 2
y = -2
500
The base of a pyramid is a rectangle with a width of 6 cm and a length of 8 cm. Find, in centimeters, the height of the pyramid if the volume is 288 cm3 .
height = 18 cm
500
In circle O, PA and PB are tangent to the circle from point P. If the ratio of the measure of major arc AB to the measure of minor arc AB is 5:1, find m∠P.
< P = 120 degrees
500
In triangle ABC, point D is on AB, and point E is on BC such that DE is parallel to AC. If DB = 2, DA = 7, and
DE = 3, what is the length of AC?
AC = 13.5
500
Prove that the diagonals of a parallelogram bisect
each other.
It's proven that the diagonals have the same midpoint.
500
In the coordinate plane, what is the total number of points 4 units from the origin and equidistant from both the x- and y-axes?