1. If the point (2,5) is shifted 3 units to the right and 2 units down in the X-Y plane, what are its new coordinates? (Hint: Movement right/left = /- X; Movement up/down = /- Y.)
The x value should be moved 3 units to the right while the x value should be moved 2 units down i.e add 3 to x value of the coordinate and subtract 2 from y value of the coordinate.
(2+3, 5 – 2)= (5, 3)
2. If the point (-1, 6) is shifted 2 units to the left and 4 units up, what are its new coordinates?
Will be moved to (-1-2, 6 + 4) = (-3, 10) this is because movement to the left implies subtraction from x value while movement upwards means addition to y value.
3. Find all the points having an x-coordinate of 3 whose distance from the point (-2, -1) is 13. (Hint: The unknown points [there are two of them] have coordinates (3, y), where y is to be determined.
Distance= 3+22+y+12=13
13=25+2y+1+y2
Square both sides
169= 25+y2+2y+1
y2+2x-143=0
Y=-b±b2-4ac2a
Y=11 or -11
The only valid value for y is 11
The coordinate is (3, 11)
4. Find all points on the y-axis that are 6 units from the point (4, -3).
Points on y axis have x value as 0. Therefore, any coordinate can be written as (0, y)
Distance= 4-02+-3-y2=6
Squaring both sides
16+9-6y+ y2=36
-11-6y+y2= 0
Y=-b±b2-4ac2a
Y= (6+80)/2 or (6 - 80)/2
=14.944/2 or-2.944/2y
Y can only be equal to -1.472
The coordinate is (0, -1.47)
No.5
No.6
3x +4y = 12
When value of x is zero 4y= 12; y=3 therefore, x intercept (0,3)
When value of y= 0 then 3x=12 ; x=4 therefore y intercept is at coordinate (4,0)
No. 7
The lines are intersecting at (-5,6)
No. 8
The lines intersect at 900
9. What is the perimeter of the rectangle with the following corners: (5,2), (-5,2) and (5,-3)? Hints: Make a sketch. Find the fourth corner. Determine the lengths of the sides by inspection; that is, by "eyeballing" the sketch.
The last coordinate is (-5,-3)
10. . Company ABC""?s profit is determined by the following equation: P = 30x+ 40y, where x and y are sales of particular products and P is in thousands of dollars. It was determined that maximum and minimum profit values occur when sales occur in the following ordered pairs: (2,6), (6,4) and (-1,-3). At which pair is the maximum profit and at which pair is the minimum ""? state the profit. Hint. A negative number = a loss, not a profit.
Solution
The highest profit can either be (2,6) or (6,4) because the remaining pair will result to a loss.
In case of (2,6) p= 30(2) +40(6) =60 +240 =300
In case of (6,4) p= 30(6) + 40 (4) = 180 +160 =340
Therefore, (6,4) is the pair which will give maximum profit.
Question 11
Finding the area
A(-2,5), B(1, 3), and C(-1,0).
Area= AxBy-Cy+Bx Cy-Ay+Cx (Ay-By)2
Area= [-2(-3-0)+ 1(0-5) +-1( 5-3)]/2
Area= 6.5
Question 12
A(-5,3), B(6, 0), and C(5,5).
Area= AxBy-Cy+Bx Cy-Ay+Cx (Ay-By)2
Area= -5 0- 5+6 5- 3+5 (-5-0)2= 6
Question 13
A(4,-3), B(0,-3), and C(4,2).
Area= AxBy-Cy+Bx Cy-Ay+Cx (Ay-By)2
Area= 4-3-2+0 2--3+4 (-3--3)2 = 10
