Number line

Correct answer: A. 5/4

Explanation: The governing number-line rule is that moving to the left decreases a coordinate, whereas moving to the right increases it. Point R has coordinate 7/2, which is 3.5 in decimal form. Since S lies 2.25 units to the left of R, subtract the distance: S = 3.5 − 2.25 = 1.25. Converting 1.25 into a fraction gives 125/100 = 5/4. Thus option A is correct. Option B, 23/4, would come from adding 2.25 and would represent movement to the right. The other options result from an incorrect subtraction or fraction conversion. The direction word “left” is therefore essential to choosing the correct operation.

Correct answer: B. A hypotenuse with legs 1 and 1

Explanation: The governing concept is the geometric construction of an irrational length using the Pythagorean theorem. Construct a right triangle whose two perpendicular legs each have length 1. Its hypotenuse is √(1² + 1²) = √(1 + 1) = √2. This length can then be transferred to the number line with a compass, giving the point representing √2. Therefore, option B is correct. Legs 1 and 2 produce √5, legs 2 and 2 produce √8, and legs 3 and 1 produce √10. Although those lengths are also valid hypotenuses of right triangles, they do not construct √2. The equal-unit-leg triangle is the required starting construction.