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secondary 3 | E Maths
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I don’t know how to solve the last part. The answer is supposed to be 11 or -5.
Date Posted: 5 years ago
Views: 476
I don’t really understand the solution
Since the y coordinate of K is 4, it means KC is a horizontal line.
So, we find area of triangle using formula ½ x base x height
Vertical height of BCK = y-coordinate of B
C - y-coordinate of B = 4 - 1 = 3 units
12 = ½ x base x height
12 = ½ x BK x 3
12 = ½ x √( (4 - 4)² + (t-3)² ) x 3
8 = √(t-3)²
8 = t - 3 or 8 = - (t - 3)
t = 11 or t = - 5
So, we find area of triangle using formula ½ x base x height
Vertical height of BCK = y-coordinate of B
C - y-coordinate of B = 4 - 1 = 3 units
12 = ½ x base x height
12 = ½ x BK x 3
12 = ½ x √( (4 - 4)² + (t-3)² ) x 3
8 = √(t-3)²
8 = t - 3 or 8 = - (t - 3)
t = 11 or t = - 5
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Now, K has the point (t, 4).
Do you realise that the y-coordinate of K is the same as the y-coordinate of C? This means that K is either directly to the left or directly to the right of C. In other words, CK is a 'horizontal' line.
The vertical height of the triangle formed is simply the difference in the y-values of B and C, which is 4 - 1 = 3.
The formula for area of a triangle is 0.5 x base x height. Since the area is given as 12 units2,
0.5 x base x 3 = 12
base = 8
This means that the base, or the length CK, is 8 units long. So K must either be 8 units to the left of C or 8 units to the right of C.
This means that the x-coordinate of K can be 8 less or 8 more than the x-coordinate of C (which is 3).
So, t can be 3 + 8 = 11 or 3 - 8 = -5.
Do you realise that the y-coordinate of K is the same as the y-coordinate of C? This means that K is either directly to the left or directly to the right of C. In other words, CK is a 'horizontal' line.
The vertical height of the triangle formed is simply the difference in the y-values of B and C, which is 4 - 1 = 3.
The formula for area of a triangle is 0.5 x base x height. Since the area is given as 12 units2,
0.5 x base x 3 = 12
base = 8
This means that the base, or the length CK, is 8 units long. So K must either be 8 units to the left of C or 8 units to the right of C.
This means that the x-coordinate of K can be 8 less or 8 more than the x-coordinate of C (which is 3).
So, t can be 3 + 8 = 11 or 3 - 8 = -5.
Date Posted:
5 years ago
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