Answers:
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Question 1) [A]: " (- 4a , 0) " .
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Question 2) [C]: " isosceles " .
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Explanation:
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Question 1) We are asked to find the coordinates for "point T".
From the graph of the trapezoid given;
Note that the "x-coordinate" given for "point A" is: "-a " .
Note that the "x-coordinate" given for "point P" is: " -3a ".
To find the "x-coordinate" for "point T" ; we calculate as follows:
" -a - 3a = -4a ".
As shown on the graph, the "y-coordinate" for "point T" is: " 0".
Hence, the coordinate for "point T" is: " (- 4a , 0 )" ;
→ which is: " Answer choice: [A]: " (- 4a , 0) " .
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Question 2): The triangle is an "isosceles" triangle.
Note: From the graph of the triangle shown, the "bottom" of the triangle; that is, from "point A to point C" is " 10a units" in length:
Note: 5a + |-5a| = 5a + 5a = 10a .
AB and BC are equal — but neither is equal to "10a" ;
{ since neither AB or BC form a diagonal of a "square"}.
By definition, an "isosceles triangle has 2 (two) equal sides ;
which is: "Answer choice: [C]: " isosceles " .
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Note: Consider the other answer choices:
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Choice [A]: "equilateral" is incorrect. Note that all equilateral triangles are isosceles triangles, but not all isosceles triangles are equilateral triangles. Equilateral triangles have 3 (three) equal sides {and 3 (three) equal angles, each of which measures 60°}. This given triangle does NOT have 3 (three) equal sides—but only two (2)— so we can rule out "Choice: [A] " .
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Choice: [B]: "right" is incorrect. This is NOT a right triangle; since there are no right angles (no "90° angles") in this triangle. So we can rule out "Choice [B] " .
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Choice: [D]: "scalene" is incorrect. A "scalene triangle" has all 3 (three) sides of different (unequal) lengths. This triangle has two (2) sides of equal length, so we can rule out "Choice: [D] " .
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Hope this helps!
Best wishes.
