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fgiga [73]
3 years ago
8

Given the points R(-4, 5) and S(2, -1). Find RS, the midpoint of RS, and point P which is 13 of the distance from R to S. Leave

your answer as a simplified radical.
Mathematics
1 answer:
lukranit [14]3 years ago
6 0

Answer:

Step-by-step explanation:

Given the points R(-4, 5) and S(2, -1), to get the distance between the points, we will use the formula;

D = √(x2-x1)²+(y2-y1)²

Given x1= -4, y1 = 5, x2 = 2 and y2 = -1

RS = √(2-(-4))²+(-1-5)²

RS = √(6)²+(-6)²

RS = √36+36

RS = √72

RS = √2×36

RS = 6√2units

To get the midpoint, we will use the formula M(X,Y) = (x1+x2/2, y1+y2/2)

(X,Y) = (-4+2/2, -1+5/2)

(X,Y) = (-2/2, 4/2)

(X,Y) = (-1,2)

Hence the midpoint is (-1,2)

To get a point P 1/3 of the distance of RS, we will multiply 1/3 with the the distance RS as shown

P = 1/3 × 6√2

P = 2√2

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Solve this equation by completing the square: x2 + 4x – 13 = –8
marishachu [46]

Answer:

x = 1 or x = -5

Step-by-step explanation:

We are given;

  • The quadratic equation, x² + 4x - 13 = -8

We are required to solve the equation using the completing square method.

To do this, we use the following steps;

Step 1: We make sure the coefficient of x² is one

x² + 4x - 13 = -8

Step 2: Combine the like terms (take the constant term to the other side)

x² + 4x - 13 = -8

x² + 4x = -8 + 13

we get

x² + 4x  = 5

Step 3: We add the square of half the coefficient of x on both sides of the equation

Coefficient of x = 4

Half of coefficient of x = 2

Square of half the coefficient of x = 2² (4)

We get;

x² + 4x + (2²)  = 5 + (2²)

Step 4: Put x and 2 under one square and the solve the other side of the equation.

We get

(x + 2)² = 5 + 4

(x + 2)² = 9

Step 5: Get the square root on both sides of the equation;

(x + 2)² = 9

√(x + 2)² = ±√9

(x + 2)= ±3

Therefore;

x+2 = + 3 or x + 2 = -3

Thus, x = 1 or -5

The solution of the equation is x = 1 or x = -5

6 0
3 years ago
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