QUESTION 1
In figure A, the area of the bigger square is [tex]625\:units^2[/tex]. This means that the length of this square is the hypotenuse of the right angle triangle formed, which is [tex]25\:units[/tex].
The area of the two smaller squares are [tex]576\:units^2[/tex] and [tex]49\:units^2[/tex].
The length of these two squares form the two shorter legs of the right angle triangle, which are [tex]24[/tex] and [tex]7[/tex] units respectively.
Therefore we can write the equation, [tex]576+49=625[/tex].
This implies that, [tex]24^2+7^2=25^2[/tex]
We can see that the sum of the squares of the two shorter legs equals the square of the longer side which is the hypotenuse and this what the Pythagoras theorem says.
But in fig. B,
[tex]5^2+4^2\ne 6^2[/tex]
Therefore the correct answer is Fig A.
QUESTION 2
See diagram.
We introduce the two lines as shown in the diagram.
From Pythagoras' Theorem,
[tex]|AB|^2=|AC|^2+|BC|^2[/tex]
But [tex]|AC|=|7-3|=4[/tex] units.
and
[tex]|BC|=|8-2|=6[/tex] units.
This implies that,
[tex]|AB|^2=4^2+6^2[/tex]
[tex]|AB|^2=16+36[/tex]
[tex]|AB|^2=52[/tex]
[tex]|AB|=\sqrt{52}[/tex]
[tex]|AB|=2\sqrt{13}[/tex]
[tex]|AB|=7.2[/tex] to the nearest tenth.
QUESTION 3
The numbers [tex]3,4[/tex] and [tex]5[/tex] form a Pythagorean triplet because [tex]3^2+4^2=5^2[/tex].
If these numbers represent the side lengths of a triangular fence, then the triangular fence must be a right angle triangle.
The correct answer is B
Yes,because [tex]3^2+4^2=5^2[/tex].
QUESTION 4
See graph.
We want to find the image of the triangle with vertices A(-5,-4), B(-2,-4), and C(-5,-1) after a reflection in the x-axis.
The mapping for this transformation is
[tex]P(x,y)\rightarrow P'(x,-y)[/tex].
We just have to negate the y-coordinates.
[tex]A(-4,-5)\rightarrow A'(-4,5)[/tex].
[tex]B(-4,-1)\rightarrow B'(-4,1)[/tex].
[tex]C(-5,-1)\rightarrow C'(-5,1)[/tex].
