7. WMA11/01 Edexcel IAL P1 June 2021 Q7 (Straight Line Graphs & Radians)
The line l1 has equation 4y + 3x = 48
The line l1 cuts the y-axis at the point C, as shown in Figure 3.
(a) State the y coordinate of C.
(1)
The point D(8, 6) lies on l1. The line l2 passes through D and is perpendicular to l1
The line l2 cuts the y-axis at the point E as shown in Figure 3.
(b) Show that the y coordinate of E is
(3)
A sector BCE of a circle with centre C is also shown in Figure 3.
Given that angle BCE is 1.8 radians,
(c) find the length of arc BE.
(3)
The region CBED, shown shaded in Figure 3, consists of the sector BCE joined to the triangle CDE.
(d) Calculate the exact area of the region CBED.
(3)
SOLUTION
a-
Method # 01
Point C is the y-intercept of line l1. So let us arrange the equation of line l1 to get y-cordinate of point C.
Hence, the y-intercept of line l1 or the y-coordinate of point C is 12.
Method # 02
Point C is the y-intercept of line l1. So put x=0 in the equation of line l1.
b-
Let us first use the two given points: the line l2 passes through D and is perpendicular to l1.
Where, m1 represents gradient of line l1 and m2 represents gradient of line l2.
So, m1=-3/4; therefore,
Now, using the point-slope formula to find the equation of line l2, where point D(8, 6) & gradient is m2=4/3.
Since E is the point where l2 cuts y-axis so the y coordinate of E is the y-intercept of line l2.
Hence, the y-coordinate of line l2 is -14/3.
c-
Using the formula of arc length of a sector.
Here the trickest part is to find the radius. The (vertical) distance between C and E is equal to radius of the sector.
Now, applying the formula of arc length.
d-
Since the traingle CDE is a right angle triangle, using the formula of area as 1/2bh. The base and height is also marked on the figure below.
Base=radius=CE
Height=x-coordinate of D=6
