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Info: - y = -(3/4)x + 9 - Area of POQ = 3 times of TOP
Since we are already have a linear equation, we can find out the x-int and the y-int of the line by setting the other to 0.
y-int = In the y=mx +b form, b is always the y-int value. In this case, b = 9. The y-int is 9. This means that side length QO is 9.
x-int = Setting the y value to 0, we get…. 0 = -(3/4)x + 9 -9 = -(3/4)x 9 = (3/4)x x = 12 The x-int is 12. This means that side length PO is also 12.
Since we know two side lengths of the triangle, we can find the are of the triangle. (9 x 12)/2 = 9 x 6 = 54 units^2.
Given that this area is three times the area of triangle TOP, we know that TOP’s area is 54/3 = 18 units^2. Plus, we know that the base of TOP is 12, so…..
(s * 12)/2 = 18 s*6 = 18 s = 3
Now, we know one of the values of (r,s). We can plug this s value back into the original equation to get an r value.
y = -(3/4)x + 9 3 = -(3/4)x + 9 -6 = -(3/4)x 6 = (3/4)x x = r = 8
Sorry Fiona, I must've missed it when you first sent it. Check it now against the solution posted this week. You can try the Balloons Away question too.
Grade 7/8 POTW We know the line y = -3/4x + 9. Since this is the y intercept, we can easily find the value of Q: y = -3/4x + 9 y = -3/4(0) + 9 y = 0 + 9 y = 0 Therefore, the coordinate of Q is (0, 9). Now we can change the equation to find the x intercept or value of P: y = -3/4x + 9 3/4x = -y + 9 3/4x/(3/4) = (-y + 9)/(3/4) x = -4/3y + 12 x = -4/3(0) + 12 x = 0 + 12 x = 12 Therefore, the coordinate of P is 12, 0. We know that OP is 12 units and OQ is 9 units, so we can now find the area of triangle POQ: (b x h)/2 = a (OP x OQ)/2 = POQ (12 x 9)/2 = POQ 108/2 = POQ 54 units squared = Area of triangle POQ We also know that POQ is 3 times the area of TOP so: POQ/3 = TOP 54/3 = TOP 18 units squared = Area of triangle TOP Since we know the base of triangle TOP, we can find the height, or the y coordinate of T: TOP = (b x h)/2 18 = (12 x h)/2 36 = 12 x h 3 = h Therefore, s is 3. Now we can just find the value of r as when y = s, x = r, and we know s = 3: y = -3/4x + 9 3 = -3/4r + 9 3/4r = 9 - 3 3/4r = 6 r = 8 Therefore, r is equal to 8, s is equal to 3, and the coordinates of T are (8, 3).
A Point of Division POTW:
ReplyDeleteInfo:
- y = -(3/4)x + 9
- Area of POQ = 3 times of TOP
Since we are already have a linear equation, we can find out the x-int and the y-int of the line by setting the other to 0.
y-int = In the y=mx +b form, b is always the y-int value. In this case, b = 9. The y-int is 9. This means that side length QO is 9.
x-int = Setting the y value to 0, we get….
0 = -(3/4)x + 9
-9 = -(3/4)x
9 = (3/4)x
x = 12
The x-int is 12. This means that side length PO is also 12.
Since we know two side lengths of the triangle, we can find the are of the triangle. (9 x 12)/2 = 9 x 6 = 54 units^2.
Given that this area is three times the area of triangle TOP, we know that TOP’s area is 54/3 = 18 units^2. Plus, we know that the base of TOP is 12, so…..
(s * 12)/2 = 18
s*6 = 18
s = 3
Now, we know one of the values of (r,s). We can plug this s value back into the original equation to get an r value.
y = -(3/4)x + 9
3 = -(3/4)x + 9
-6 = -(3/4)x
6 = (3/4)x
x = r = 8
The coordinates (r,s) is equal to (8,3)
did my answer to the potw not upload?
ReplyDeleteSorry Fiona, I must've missed it when you first sent it. Check it now against the solution posted this week. You can try the Balloons Away question too.
DeleteGrade 7/8 POTW
ReplyDeleteWe know the line y = -3/4x + 9. Since this is the y intercept, we can easily find the value of Q:
y = -3/4x + 9
y = -3/4(0) + 9
y = 0 + 9
y = 0
Therefore, the coordinate of Q is (0, 9). Now we can change the equation to find the x intercept or value of P:
y = -3/4x + 9
3/4x = -y + 9
3/4x/(3/4) = (-y + 9)/(3/4)
x = -4/3y + 12
x = -4/3(0) + 12
x = 0 + 12
x = 12
Therefore, the coordinate of P is 12, 0. We know that OP is 12 units and OQ is 9 units, so we can now find the area of triangle POQ:
(b x h)/2 = a
(OP x OQ)/2 = POQ
(12 x 9)/2 = POQ
108/2 = POQ
54 units squared = Area of triangle POQ
We also know that POQ is 3 times the area of TOP so:
POQ/3 = TOP
54/3 = TOP
18 units squared = Area of triangle TOP
Since we know the base of triangle TOP, we can find the height, or the y coordinate of T:
TOP = (b x h)/2
18 = (12 x h)/2
36 = 12 x h
3 = h
Therefore, s is 3. Now we can just find the value of r as when y = s, x = r, and we know s = 3:
y = -3/4x + 9
3 = -3/4r + 9
3/4r = 9 - 3
3/4r = 6
r = 8
Therefore, r is equal to 8, s is equal to 3, and the coordinates of T are (8, 3).
What do you think the level of difficulty was here? How come you didn't try the second challenge question? (called "Balloons Away")
Delete