geometry b - unit 1: exam

ab has endpoints at a(−6, −3) and b(2, 7). what are the coordinates of the midpoint, m, of the segment?

(-2, 2)

line segment ba has endpoints b(−6, 0) and a(4, 5). what are the coordinates of the point located 3/5 of the way from point a to point b?

(-2, 2)

line segment ba has endpoints b(−6, 3) and a(−1, 8). what are the coordinates of the point located 1/5 of the way from b to a?

(-5, 4)

line segment ab has endpoints a(−2, 6) and b(4, −6). what are the coordinates of the point that partitions ba according to the part-to-part ratio 2:4?

(2, -2)

ab has endpoints a and b with point a at (6,5). ab has midpoint m at (4,6). what are the coordinates of point b?

(2, 7)

heather is given the coordinates of the vertices of quadrilateral abcd. he is asked to prove whether the quadrilateral is a parallelogram. her proof follows the diagram.

1. given 2. midpoint formula 3. if two lines intersect, then their intersection is exactly one point. 4. definition of midpoint 5. definition of bisect 6. if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

given: quadrilateral efgh has vertices at e(5, -4), f(6, 1), g(2, 7), and h(1, 2) prove: quadrilateral efgh is a parallelogram. match each numbered statement with the correct reason.

1. given 2. slope formula 3. lines with equal slopes are parallel. 4. both pairs of opposite sides of a parallelogram are parallel.

which information about the coordinates of b will prove that mc is a median of △abc?

the coordinates of b are (9, 11).

what is the equation of the line, in slope-intercept form, that is perpendicular to the line with the equation y = 6x − 1 and passes through the point (−6, 4)?

y = -1/6x + 3

what is the equation of the line that is parallel to y − 5 = −1/3(x + 2) and passes through the point (6, −1)?

y = -x/3 + 1

what is the equation of the line that is perpendicular to line with the equation y = −3x − 1 and passes through the point (6, −1)?

y = 1/3x - 3

what is the equation of the line that is parallel to y = 6x − 1 and passes through the point (−3, 4)?

y = 6x + 22

is line g perpendicular to line h? why or why not?

yes, because the slopes of lines gg and hh are opposite and reciprocal.

given: quadrilateral efgh has vertices at e(7, 4), f(5, 7), g(3, 3), and h(5, 0). prove: quadrilateral efgh is a parallelogram. match each numbered statement with the correct reason.

1. given 2. slope formula 3. lines with equal slopes are parallel. 4. both pairs of opposite sides of a parallelogram are parallel.

line f has a slope of −6/3, and line g has a slope of −8/4. what can be determined about distinct lines f and g?

XXX the lines will intersect.

if you can show two similar triangles, you can use the proportional relationship between the side lengths of the triangles with the definitions of slope and opposite reciprocals to show that the slopes of the two perpendicular lines are opposite reciprocals. which pair of triangles can be proved similar to complete the proof?

XXX △njh ∼ △nqp

which information about the coordinates of g and h will prove that gh is a midsegment of △def?

g(1.5, 2) and h(6.5, -3)

which of the following describes how izan can prove that the slopes of mn and kl are the same?

izan can use the slope formula to show the slope of mn = -mo/no and the slope of kl = -ko/lo. by substitution, the slope of mn = the slope of kl

given: △abe has vertices at a(3,7), b(7,3), and e(1,5). prove: △abe is a right triangle match each numbered statement with the correct reason.

1. given 2. slope formula 3. multiply 4. if the product of the slopes of two nonvertical lines is −1 the lines are perpendicular. 5. perpendicular lines intersect to form right angles. 6. definition of right triangle

given: quadrilateral efgh has vertices at e(2,3), f(-2,5), g(-3,3), and h(1,1) prove: quadrilateral efgh is a rectangle. match each numbered statement with the correct reason.

1. given 2. slope formula 3. multiply 4. if the product of the slopes of two nonvertical lines is −1 the lines are perpendicular. 5. perpendicular lines intersect to form right angles. 6. if a quadrilateral has four right angles, then it is a rectangle.