Question

12 multiple choice 2 points if the length of one of the legs of a right triangle is 10 and the length of the other leg is 24, what is the length of the hypotenuse? 13 17 169 26 13 multiple choice 2 points what are the coordinates of a, the image of point a(-3, 4), after a rotation of 180° about the origin? (3, 4) (-4, -3) (4, -3) (3, -4) 14 multiple choice 2 points what is the measure of angle r? triangle image with angle q 92°, angle s 59° 29° 39° 17° 31° 15 multiple choice 2 points the three vertices of △abc are in quadrant i. if △abc is reflected in the x - axis, its image will lie in quadrant iii iv ii i

Explanation:

Question 12 Step1: Apply Pythagorean theorem

Let hypotenuse = $c$, legs $a=10$, $b=24$. Formula: $c=\sqrt{a^2+b^2}$

Question 12 Step2: Calculate value

$c=\sqrt{10^2+24^2}=\sqrt{100+576}=\sqrt{676}=26$

Question 13 Step1: Use 180° rotation rule

Rule: $(x,y)\to(-x,-y)$ for origin rotation

Question 13 Step2: Substitute coordinates

For $A(-3,4)$: $A'=(-(-3), -4)=(3,-4)$

Question 14 Step1: Triangle angle sum property

Total angles = $180^\circ$. Let $\angle R = x$

Question 14 Step2: Solve for $x$

$x=180^\circ - 92^\circ - 59^\circ=29^\circ$

Question 15 Step1: Apply x-axis reflection rule

Rule: $(x,y)\to(x,-y)$; Quadrant I: $(+,+)$

Question 15 Step2: Identify new quadrant

Reflected point: $(+,-)$, which is Quadrant IV

Answer:

1. D. 26
2. D. (3, -4)
3. A. 29°
4. B. IV