Lesson #1 – Precalculus

Plot the points A(2, 5), B(−3, −1), C(0, 4), D(4, −2) on the coordinate plane. Which quadrant does each point lie in?

• A(2, 5) is in Quadrant I, B(−3, −1) is in Quadrant III, C(0, 4) is on the y-axis, D(4, −2) is in Quadrant IV.

• A(2, 5) is in Quadrant II, B(−3, −1) is in Quadrant I, C(0, 4) is in Quadrant IV, D(4, −2) is in Quadrant III.

• A(2, 5) is in Quadrant III, B(−3, −1) is in Quadrant II, C(0, 4) is in Quadrant I, D(4, −2) is in Quadrant II.

• A(2, 5) is in Quadrant IV, B(−3, −1) is in Quadrant IV, C(0, 4) is in Quadrant III, D(4, −2) is in Quadrant I.

Tags

CCSS.6.NS.C.6B

A triangle has vertices at P(1, 2), Q(4, 2), R(3, −1). Translate the triangle up 3 units and left 2 units. Then write the coordinates of the new vertices P', Q', R'.

• P'(−1, 5), Q'(2, 5), R'(1, 2)

• P'(3, 5), Q'(6, 5), R'(5, 2)

• P'(1, 5), Q'(4, 5), R'(3, 2)

• P'(−1, 2), Q'(2, 2), R'(1, −1)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Find the distance between the points M(2, −3) and N(−4, 1). (Use a calculator to find the square root)

• The distance is 7.21 units (rounded to two decimal places).

• The distance is 5.00 units (rounded to two decimal places).

• The distance is 8.00 units (rounded to two decimal places).

• The distance is 6.40 units (rounded to two decimal places).

Tags

CCSS.HSG.GPE.B.7

Determine whether the points A(0, 0), B(3, 4), C(3, 0) form a right triangle. Show work using the distance formula.

• Yes, the points form a right triangle. The side lengths are 5, 4, and 3 units, satisfying the Pythagorean theorem.

• No, the points do not form a right triangle. The side lengths do not satisfy the Pythagorean theorem.

• Yes, the points form an equilateral triangle with all sides equal.

• No, the points form an isosceles triangle but not a right triangle.

Tags

CCSS.HSG.GPE.B.7

Find the midpoint of the line segment connecting X(6, 2) and Y(−2, 8).

• The midpoint is (2, 5).

• The midpoint is (4, 6).

• The midpoint is (3, 7).

• The midpoint is (0, 3).

Tags

CCSS.HSG.GPE.B.6

Plot the points A(−2, 6), B(5, −3), C(−4, −2), D(0, −5) on the coordinate plane. Which quadrant does each point lie in?

• A(−2, 6): Quadrant II; B(5, −3): Quadrant IV; C(−4, −2): Quadrant III; D(0, −5): Lies on the y-axis (not in any quadrant)

• A(−2, 6): Quadrant I; B(5, −3): Quadrant III; C(−4, −2): Quadrant II; D(0, −5): Quadrant IV

• A(−2, 6): Quadrant III; B(5, −3): Quadrant II; C(−4, −2): Quadrant I; D(0, −5): Quadrant I

• A(−2, 6): Quadrant IV; B(5, −3): Quadrant I; C(−4, −2): Quadrant IV; D(0, −5): Quadrant II

Tags

CCSS.6.NS.C.6B

A triangle has vertices at P(−1, 0), Q(2, −3), R(4, 1). Translate the triangle down 2 units and right 3 units. Then write the coordinates of the new vertices P', Q', R'.

• P'(2, −2), Q'(5, −5), R'(7, −1)

• P'(1, 2), Q'(4, -1), R'(6, 3)

• P'(2, 0), Q'(5, -3), R'(7, 1)

• P'(0, -2), Q'(3, -5), R'(5, -1)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Find the distance between the points M(−3, 2) and N(4, −1).

Tags

CCSS.HSG.GPE.B.7

Find the midpoint of the line segment connecting X(−5, −3) and Y(7, 9).

• Midpoint = ((−5+7)/2, (−3+9)/2) = (1, 3)

• Midpoint = ((−5−7)/2, (−3−9)/2) = (−6, −6)

• Midpoint = ((−5+7)/2, (−3−9)/2) = (1, −6)

• Midpoint = ((−5−7)/2, (−3+9)/2) = (−6, 3)

Tags

CCSS.HSG.GPE.B.6

Which quadrant does the point (–3, 7) lie in?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Tags

CCSS.6.NS.C.6B