1.A right triangle has leg of b of length 7 and a hypotenuse of length 11. What is a length of the other leg, a? Round to the nearest tenth if necessary. (1 point)
A. 2.0
B. 8.5
C. 13.0
D. 9.6
2. Find the length of a line segment CD with endpoint C at (-3,1) and endpoint D at (5,6). Round your answer to the nearest tenth, if necessary. (1 point)
A 9.4
B 5.4
C 3.6
D 11.7
3.Find the midpoint of a segment FG with point F at (-6,4) and point G at (8,-2). (1 point)
A (-7,3)
B (7,-3)
C (1,1)
D (-1,-1)
To solve these questions, we will use the appropriate formulas and methods. Let's break down each question step by step to find the correct answers.
1. In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the hypotenuse. This is known as the Pythagorean theorem. In this question, we are given the length of one leg (b = 7) and the hypotenuse (c = 11).
By using the Pythagorean theorem, we can find the length of the other leg (a). The formula is:
a^2 + b^2 = c^2
Substituting the given values:
a^2 + 7^2 = 11^2
a^2 + 49 = 121
Now, let's solve for a:
a^2 = 121 - 49
a^2 = 72
Taking the square root of both sides, we get:
a ≈ √72
a ≈ 8.5
Therefore, the length of the other leg (a) is approximately 8.5. So, the correct answer is option B.
2. To find the length of a line segment between two points, we can use the distance formula. The distance formula is:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
In this question, we are given the coordinates of the endpoints C(-3, 1) and D(5, 6).
Substituting these values into the distance formula, we get:
d = √[(5 - (-3))^2 + (6 - 1)^2]
d = √[(5 + 3)^2 + (6 - 1)^2]
d = √[8^2 + 5^2]
d = √[64 + 25]
d ≈ √89
Therefore, the length of the line segment CD is approximately √89. Rounding to the nearest tenth, the correct answer is approximately 9.4. So, the correct answer is option A.
3. To find the midpoint of a line segment, we can use the midpoint formula. The midpoint formula is:
((x1 + x2)/2, (y1 + y2)/2)
In this question, we are given the coordinates of the endpoints F(-6, 4) and G(8, -2).
Substituting these values into the midpoint formula, we get:
(((-6) + 8)/2, (4 + (-2))/2)
(2/2, 2/2)
(1, 1)
Therefore, the midpoint of the line segment FG is (1, 1). So, the correct answer is option C.
#1: √(11^2 - 7^2)
#2: √((5+3)^2 + (6-1)^2)
#3: ((-6+8)/2,(-2+4)/2)
Better review your text for these topics.