geometry b - unit 2: coordinate geometry distance formula lessons 6-10

lesson 6

distance in the coordinate plane

examine the diagram to answer the question. what is the equation of the circle?

x^2 + y^2 = 25

lesson 10

coordinate proofs with distance formula

lesson 9

rewrite equations of circles

2. what is the area of △abc?

16 units

what is the area of the square when rounded to the nearest whole number?

17 units

approximately how many units is the perimeter of abc?

19.8

examine the diagram, and answer the question. the points a(2, 7) and b(−4, −3) are located in the coordinate plane as shown. what is the distance between the two points?

2√34

△abc has vertices at a(8, 3), b(8, 5), and c(4, 3). what is the area of △abc?

4.0 units

examine the diagram and information to answer the question. square abcd has vertices at a(−1, 3), b(0, 7), c(4, 6), and d(3, 2) how many units is the perimeter of square abcd?

4√17

points a(−6, 1) and b(0, 4) are located in a coordinate plane. what is the distance from a to b?

6.7

lesson 8

equations of circles

lesson 7

perimeter and area

a circle has the equation (x + 9)^2 + (y + 3)^2 = 96 what is the center and the radius of the circle?

the center is (-9, -3) and the radius is 4√6 units

a circle has the equation (x - 4)^2 + (y - 1)^2 = 34 what are the coordinates of the center and the length of the radius?

the center is at (4, 1) and the radius is √34 units.

a circle has the equation (x + 11)^2 + (y + 6)^2 = 324. what are the coordinates of the center and the length of the radius?

the coordinates of the center are (-11, -6), and the length of the radius is 18 units

which answer verifies whether p lies on circle c?

the equation (2 + 2)^2..... is a true statement, so p is on circle c

a circle has the equation x^2 + y^2 + 16y - 30x = 0 what is the equation of the circle in standard form, the coordinates of its center, and the length of its radius?

the equation of the circle is (x - 15)^2 + (y + 8)^2 = 289; the center is at (15, -8), and the radius is 17 units.

a circle has the equation x^2 - 12x + 27 = -y^2 + 8y what is the equation of the circle in standard form, the location of its center, and the length of its radius?

the equation of the circle is (x - 6)^2 + (y - 4)^2 = 25; the center is at (6, 4), and the radius is 5 units

which answer verifies whether the point p(12, -2) is on circle c?

the statement (9 - 6)^2... is a true statement, so p is not on circle c

checpoint: what is the equation of the circle? match the expression or equation to the steps used to find the equation of the circle.

vertical leg: |y - 1| horizontal leg: |x - 4| pythagorean theorem: (x - 4)^2 + (y - 1)^2 = 3^2

what is the equation of the circle? match the expression or equation to the steps used to find the equation of the circle.

vertical leg: |y - 4| horizontal leg: |x - 5| pythagorean theorem: (x - 5)^2 + (y - 4)^2 = 5^2

a circle has the equation x^2 + 12y + 22x + y^2 - 167 = 0 what is the equation of the circle in standard form?

(x + 11)^2 + (y + 6)^2 = 324

which answer verifies that the point p(6, -12) is on the circle?

(5 - 6)^2 + (-15 + 12)^2 = (5 - 2)^2 + (-15 + 14)^2

examine the diagram and information to answer the question what is the equation of the circle?

(x - 4)^2 + (y + 2)^2 = 25

what is the approximate perimeter of △abc?

14.2

△abc has vertices at a(−1, 1), b(−7, 1) and c(−3, 6). what is the area of △abc?

15 units

a circle has the equation x^2 + y^2 - 8x - 2y - 17 = 0 what is the equation of the circle in standard form?

(x - 4)^2 + (y - 1)^2 = 34

complete the square to rewrite the equation in the form (x − h)^2 = p. x^2 - 14x - 95 = 0 what is the equation?

(x - 7)^2 = 144

match each numbered statement with its correct reason.

1. given 2. distance formula 3. transitive property of equality 4. definition of congruence 5. if both sets of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

if c(8, −1) and d(−2, 3), what is the approximate distance between the two points?

10.8

examine the diagram and information to answer the question. parallelogram efgh has vertices at e(1, 3), f(0, 2), g(4, 0), and h(5, 1) how many units is the perimeter of parallelogram efgh?

2√2 + 4√5

examine the diagram, and answer the question. the points a(4, −2) and b(−1, 1) are located in the coordinate plane as shown. what is the approximate distance between the two points?

5.8

examine the diagram, and answer the question. the diagram shows a(−3, 5) and b(8, 1). what is the distance between the points?

11.7

examine the diagram, and answer the question. the points a(2, 7) and b(−4, −3) are located in the coordinate plane as shown. what is the approximate distance between the two points?

11.7

select two answers: one for question a, and one for question b.

a: (13, 1) b: 2

the points a(−3, 5) and b(1, −2) are located in a coordinate plane. what is the approximate distance between the two points?

8.1

how many units is the perimeter of square abcd?

8√13

which methods can be used to prove that quadrilateral abcd is a parallelogram? select all that apply

prove ab || cd and bc || ad by using the slope formula and the relationship of the slopes of parallel lines. prove ad and bc have equal slopes and are therefore parallel, by using the slope formula. then prove ad = bc by using the distance formula and the definition of congruent segments.

examine the diagram, and answer the question. the diagram shows a(−3, 5) and b(8, 1). what is the distance between the two points?

√137

complete the square to rewrite the equation in the form (x − h)^2 = p. x^2 + 6x - 18 = 0 what is the equation?

(x + 3)^2 = 27

what is the equation of a circle with its center at (−6, −3) and a radius of 12?

(x + 6)^2 + (y + 3)^2 = 144

3. what is the area of △abc?

15 units

examine the diagram and information to answer the question. what is the equation of the circle?

(x + 9)^2 + (y - 10)^2 = 9

what is the area of rectangle efgh?

10 units

which answers can be used to prove that quadrilateral abcd is a parallelogram? select all that apply

ab = dc and ab || dc slope of ab = slope of dc, ab = dc ab = dc and ad = bc

complete the square to rewrite the equation in the form (x - h) = p. x^2 - 4x - 75 = 0 what is the equation?

(x - 2)^2 = 79

complete the square to rewrite the equation in the form (x - h) = p. x^2 - 6x - 33 = 0 what is the equation?

(x - 3)^2 = 42