What is a "Slope, Midpoint & Distance"? This is the problem:
(7,3) and (-1,-4)
slope = (Y2-Y1)/(X2-X1)
=(-4-3)/-1-7
= -7/-8
=7/8
midpoint
x = X1 + (1/2)(X2-X1) = 7 +(1/2)(-8)
= 7-4
= 3
do y the same way
d^2 = (Y2-Y1)^2 + (X2-X1)^2
d^2 = 49+64 = 113
d = sqrt (113)
"Slope, Midpoint & Distance" refers to three different concepts used in geometry and algebra.
1. Slope: Slope is a measure of how steep a line is. It describes the rate at which the line increases or decreases as you move along it. The formula to calculate slope is (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the coordinates of two points on the line.
To find the slope between the points (7, 3) and (-1, -4), you can use the formula. Let's call (x₁, y₁) = (7, 3) and (x₂, y₂) = (-1, -4).
Slope = (-4 - 3) / (-1 - 7)
= -7 / -8
= 7/8
So, the slope between the points (7, 3) and (-1, -4) is 7/8.
2. Midpoint: Midpoint is the point that lies exactly halfway between two given points. To find the midpoint, you take the average of the x-coordinates and the average of the y-coordinates of the two points.
To find the midpoint between the points (7, 3) and (-1, -4), you can use the formula. Let's call (x₁, y₁) = (7, 3) and (x₂, y₂) = (-1, -4).
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
= ((7 + (-1)) / 2, (3 + (-4)) / 2)
= (6 / 2, -1 / 2)
= (3, -1/2)
So, the midpoint between the points (7, 3) and (-1, -4) is (3, -1/2).
3. Distance: Distance is the length between two points. It can be found using the distance formula, which is derived from the Pythagorean theorem. The distance formula is √[(x₂ - x₁)² + (y₂ - y₁)²], where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
To find the distance between the points (7, 3) and (-1, -4), you can use the formula. Let's call (x₁, y₁) = (7, 3) and (x₂, y₂) = (-1, -4).
Distance = √[(-1 - 7)² + (-4 - 3)²]
= √[(-8)² + (-7)²]
= √[64 + 49]
= √113
So, the distance between the points (7, 3) and (-1, -4) is √113, which is approximately 10.63.