This question is pertaining to College Algebra

Question

For the points P and Q, find (a) the distance d (P,Q) and (b) the coordinates of the midpoint m of line segment PQ.

 

P(- 4, 3), Q(2, -5)

 

P(- the square root of 7, 8* the square root of 3) , Q(5* the square root of 7, - the square root of 3)

Answer 1

Hey, Keissa. To find the distance D between two points (x₁, y₁) and (x₂, y₂), use the Distance Formula:

 

D = sqrt [(y₂ - y₁)² + (x₂ - x₁)²]

 

= sqrt [(-5 - 3)² + (2 - (-4))²]

 

= sqrt [(-8)² + 6²] = sqrt (64 + 36) = sqrt (100) = 10

 

The Midpoint Formula states that given two points (x₁, y₁) and (x₂, y₂), then the midpoint M is defined as:

 

M = {(x₁ + x₂)/2 , (y₁ + y₂)/2}

 

The x-coordinate of the midpoint is (-4 + 2)/2 = -2/2 = -1

 

The y-coordinate of the midpoint is (3 + (-5))/2 = -2/2 = -1

 

So the midpoint is (-1, -1)