Grade 10 Math Take Home Test #6

NAME:______

Grade 10 Math Take home test #6 Monday February 13th , 2012

Instructions:  Please answer each of the questions below in the space provided.  Please show all your work  The test will be marked out of 100  Late tests will lose 5 marks per day. ______

Good luck! 1. Write each of the following equations in standard form. Then, state the slope, the y-intercept, the zero(s), the domain, the range, the variation and the sign, and sketch them on the graph provided. a) 2x+3y-7=0

b) 4x – 3y = 12 3x 4y c)  1 5 7

d) 5x  3y  9 2. Find the equation of the line satisfying each of the following statements. a) a line of slope -3 and y-intercept of 5.

7 b) a line of slope and passing through P(0,8) 9

 3 c) a line of slope and passing through P(7,8) 5

d) A line through R (2,-5) and S(11, -2)

e) a line through A(1,0) and B(0, -6)

f) a line parallel to y=4x-3 and passing though P(5,6) g) a line perpendicular to y=4x-3 and passing though P(5,6)

3. Find the equation of the lines shown in each of the following graphs. a)

4. Consider each of the graphs below. a) Which of the following equations match the lines A and B? 1. y = 4 - 2 x 2. y = (2/3)x + 14 3. y = 1/2 x + 4 4. y = 4 + 2 x 5. y = 14 - (3/2) x

6. y = 14 - (2/3) x

b) Which of the following equations matches the lines A, B, and C.

1. y = 4 + (1/3) x 2. y = 6 3. y = -1/3 + 4 x 4. y = x + 6 5. y = 4 - (1/3) x

6. y = (3/2)x + 2

5. State the relationship between each of the following sets of lines (i.e. parallel, perpendicular, coincident, or intersecting).Please explain your reasoning. a) L1: y=3x+4 L2: y=3x+7

b) L1: y=-4x+1 L2: 4y=x+3

c) L1: y=2x-5 L2: y=-5x+2

d) L1: 3y=-x+2 L2: y=3x-5

e) L1: 9x+12y-36=0 x y L2:  1 4 3 6. A right trapezoid has been drawn in the Cartesian plane below. The coordinates of each vertex are indicated.

A(0,5) B(3,5)

D(0,0) C(5,0) a) Find the coordinates of M1 and M2, respectively located at the midpoints of AD and BC.

b) Show that the segment that connects the two midpoints of the non-parallel side of a right trapezoid is parallel to the bases of the trapezoid. (Please explain the steps taken to answer this question). c) Show that the length of the segment connecting the midpoints of the two non-parallel sides of a right trapezoid is equal to half the sum of the length of its bases. (Please explain the steps taken to answer this question). 7. Given the following information:

Line 1: x-intercept is 5 Line 2: x-intercept is -7 y-intercept is -3 y-intercept is -1

If line 1 and line 2 represented the shore lines of two beaches, and you are a swimmer at point P (10,11) being chased by a shark, which beach should you try to swim to, and why? Please explain the steps taken to answer this question

8. Given points A(3,4), B(-1,2) and C(8,-1): a) Find the distance between point A, and the line passing through BC. b) Find the area of the triangle formed by the points ABC where BC is the base of the triangle.

9. Given the rectangle formed by the points A(1,2), B(1,5), C(7,5) and D(7,2), show that the two diagonals AC and BD cross each other at their midpoints.