12. What is the distance between P(–4, 3) and Q(6, 1)? Round to the nearest tenth.
can someone please explain how to do this problem please
draw horizontal and vertical lines from the two points to form a rectangle. The distance between them is just the diagonal of the rectangle. That is why the distance formula is
d = √(10^2+2^2) = √104
The distance formula is just the Pythagorean theorem value.
To find the distance between two points in a coordinate plane, you can use the distance formula. The distance formula is derived from the Pythagorean theorem.
Here's how you can find the distance between points P(-4, 3) and Q(6, 1):
1. Start by identifying the coordinates of the two points: P (-4, 3) and Q (6, 1).
2. Use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
3. Plug in the values into the formula:
Distance = √((6 - (-4))^2 + (1 - 3)^2)
= √((10)^2 + (-2)^2)
= √(100 + 4)
= √104
4. To round to the nearest tenth, evaluate the square root to decimal places:
Distance ≈ √104 ≈ 10.2
Therefore, the distance between P(-4,3) and Q(6,1) is approximately 10.2 units.
To find the distance between two points in a coordinate plane, you can use the distance formula. Here are the steps to solve this problem:
Step 1: Identify the coordinates of each point. In this case, point P has coordinates P(-4, 3) and point Q has coordinates Q(6, 1).
Step 2: Apply the distance formula. The distance formula is sqrt((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the formula becomes:
sqrt((6 - (-4))^2 + (1 - 3)^2)
Step 3: Simplify the equation under the square root:
sqrt((10)^2 + (-2)^2)
Step 4: Calculate the value inside the square root:
sqrt(100 + 4)
Step 5: Simplify the equation:
sqrt(104)
Step 6: Round the answer to the nearest tenth:
The square root of 104 is approximately 10.2.
Therefore, the distance between points P(-4, 3) and Q(6, 1) is approximately 10.2 units.