Need help with these--
21. Find the possible values of a, of the distance between the points is 5, and the coordinates are (1, 1) and (4,a)
22. The Pythagorean Theorem works only for _______ triangles.
Right?
25. Three sides of a triangle are 2, 4, and 8. The two smallest sides of a similar triangle are 4 and 8. What is the measure of the missing side?
16?
Thanks
-MC
#22 and #25 = correct
#21 use the distance formula:
d = square root of [(x2-x1)^2+(y2-y1)^2]
where the coordinates are (x1,y1) and (x2,y2)
For your problem d = 5.... now you plug all the numbers in that equation and solve for y2.
Sure, I can help you with these questions. Let's go through each one step by step.
21. To find the possible values of 'a' for the distance between the points (1, 1) and (4, a) to be 5, we can use the distance formula. The distance formula is given by:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points, and 'd' is the distance between them.
In this case, we have (x₁, y₁) = (1, 1) and (x₂, y₂) = (4, a). So the distance formula becomes:
5 = √[(4 - 1)² + (a - 1)²]
We square both sides to eliminate the square root:
25 = (4 - 1)² + (a - 1)²
25 = 9 + (a - 1)²
Subtracting 9 from both sides, we get:
16 = (a - 1)²
Now we take the square root of both sides:
√16 = √(a - 1)²
±4 = a - 1
Simplifying further, we have two possible cases:
Case 1: a - 1 = 4
a = 4 + 1
a = 5
Case 2: a - 1 = -4
a = -4 + 1
a = -3
Therefore, the possible values of 'a' are 5 and -3.
22. The Pythagorean Theorem works only for right triangles. A right triangle is a triangle that has one angle measuring 90 degrees (a right angle). The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
So, to use the Pythagorean Theorem, you need to have a triangle with a 90-degree angle.
25. In this question, we are given the lengths of three sides of a triangle: 2, 4, and 8. We are also told that the two smallest sides of a similar triangle are 4 and 8. We need to find the measure of the missing side.
To solve this, we need to understand the concept of similar triangles. Similar triangles have the same shape but possibly different sizes. Corresponding sides of similar triangles are proportional.
In the given triangle, the sides are in the ratio 1:2:4 (2:4:8). Since the two smallest sides of the similar triangle are 4 and 8, we can say that the ratio of the sides of the similar triangle is also 1:2:4.
Let's call the missing side 'x'. Since the smallest side in the original triangle is 2, and the smallest side in the similar triangle is 4, we can set up a proportion:
2/4 = x/8
Cross-multiplying, we get:
2*8 = 4*x
16 = 4x
Dividing both sides by 4, we find:
x = 4
So, the measure of the missing side in the similar triangle is 4.
I hope this clarifies the answers to your questions. Let me know if there's anything else I can assist you with!