Question

1.) Which of the following is the correct equation for the Pythagorean Theorem, where a and b are the side lengths and c is the length of the hypotenuse?

a.) (a+b)^2=c^2
b.) a^2+b^2=c^2
c.) a^2-b^2=c^2
d.) (a-b)^2=c^2

3.) Find the distance between the points (9, −7) and (5, −4).(1 point)

a.) 5
b.) 25
c.) √7
d.) √137

4.) To find the distance between (17, 3) and (17, −5), Marcia used the following equation. Is Marcia correct? Explain.

D = | 3 − (−5) | = 8

a.) Marcia is not correct. Since the points are in two-dimensions, the distance formula must be used to find the distance.

b.)Marcia is correct. For any pair of points, the distance between the points can be treated as if they are in one-dimension.

c.)Marcia is correct. Since the x-coordinates are the same, the distance between the points can be treated as if they are in one-dimension.

d.)Marcia is not correct. According to the distance formula, the distance should be D=√(17-17)^2+(3-(-5))^2=√8

Answer 1

Option d for question 4 should be:

d.)Marcia is not correct. According to the distance formula, the distance should be D=√(17-17)^2+(3-(-5))^2=8

Answer:

1. (b)  a^2+b^2=c^2

3. (a) 5

4. (d) Marcia is not correct. According to the distance formula, the distance should be D=√(17-17)^2+(3-(-5))^2=8

Step-by-step explanation:

(1) From Pythagoras' theorem, the square of the hypotenuse side of a given right-angled triangle, is equal to the sum of the squares of the other two sides. Now, if the other two sides are a and b, and the hypotenuse is c, then using this theorem, the following holds:

c² = a² + b²

(2) The distance D, between two points (a, b) and (c, d) is given by;

D = √(a-c)² + (b-d)²        ----------------(i)

From the question, the points given are (9, -7) and (5, -4):

This means that;

a = 9

b = -7

c = 5

d = -4

Substitute these values into equation (i) and get;

D = √(9-5)² + (-7- (-4))²

D = √(4)² + (-3)²

D = √16 + 9

D = √25

D = 5

Therefore, the distance between these points is 5 units

(4) As explained in question 3 above, Maria is not correct. To find the distance between two points, we use the relation shown in the answer to question 3 above. i.e

D = √(a-c)² + (b-d)²

Since the given points are (17, 3) and (17, -5), it implies that;

a = 17

b = 3

c = 17

d = -5

D = √(17-17)² + (3-(-5))²

D = √(0)² + (8)²

D = √8²

D = 8