Given the points below, find the distance from X to Y. Round to the nearest hundredth.
X(-9,2) and Y(5, -4)
We can use the distance formula to find the distance from X to Y:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the given coordinates:
d = √((5 - (-9))^2 + (-4 - 2)^2)
d = √((14)^2 + (-6)^2)
d = √(196 + 36)
d = √232
d ≈ 15.23
So the distance from X to Y is approximately 15.23.
<1 and <2 are supplementary angles. m<1 is 2y+12 and the m<2 is 8y+8. Find m<2.
If angles 1 and 2 are supplementary, their measures add up to 180 degrees.
So, we have the equation:
m<1 + m<2 = 180
Plugging in the given measures:
2y + 12 + 8y + 8 = 180
Combining like terms:
10y + 20 = 180
Subtracting 20 from both sides:
10y = 160
Dividing both sides by 10:
y = 16
Now that we have the value of y, we can find the measure of angle 2:
m<2 = 8y + 8
m<2 = 8(16) + 8
m<2 = 128 + 8
m<2 = 136
Therefore, the measure of angle 2 is 136 degrees.
To find the distance between two points in a coordinate plane, you can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's substitute the coordinates of X and Y into the formula:
Distance = √((5 - (-9))^2 + (-4 - 2)^2)
Simplifying further:
Distance = √((5 + 9)^2 + (-4 - 2)^2)
Distance = √((14)^2 + (-6)^2)
Calculating the square of each term:
Distance = √(196 + 36)
Distance = √(232)
Lastly, round the result to the nearest hundredth:
Distance ≈ 15.23
Therefore, the distance from point X to point Y is approximately 15.23 units.
To find the distance between two points in a 2D Cartesian coordinate system, you can use the distance formula. The distance formula is based on the Pythagorean theorem and states that the distance between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, we have the coordinates of point X as (-9, 2) and the coordinates of point Y as (5, -4).
Let's substitute these values into the distance formula:
d = sqrt((5 - (-9))^2 + (-4 - 2)^2)
First, simplify the expression inside the square root:
d = sqrt((14)^2 + (-6)^2)
Next, calculate the values inside the parentheses:
d = sqrt(196 + 36)
Combine like terms:
d = sqrt(232)
Finally, find the square root of 232 using a calculator or by approximating it:
d ≈ 15.23
Therefore, the distance from point X to point Y is approximately 15.23 units, rounded to the nearest hundredth.