At point A(-2,5) a line with a slope of -1/2 is drawn to point B. What are the coordinates of point B?

Question

I need the answer as fast as a lightening bolt. Thanks 

Answer 1

Use this formula for slope.

 

Slope = (y₂ - y₁) / (x₂ - x₁)

 

Let Point A = (x₁ , y₁)

Let Point B = (x₂ , y₂)

 

 

Plug in these values into the slope formula.

 

-1 / 2 = (y₂ - 5) / (x₂ - (-2))

 

-1 / 2 = (y₂ - 5) / (x₂ + 2)

 

 

Now we break this up into two separate equations.

 

-1 = y₂ - 5                    and               2 = x₂ + 2

 

4 = y₂                          and               0 = x₂

 

 

This makes (0, 4) the coordinates of point B.

 

 

Answer 2

Though technically B could be anywhere on the Cartesian plane as long as it is within the line Y= -(1/2)X + 4 we can find this point through several routes:

• I am working under the assumption that you want point (B) so that we can use it to develop the provided slope. 
• Hence in this case we would find and apply the Formula for our slope for two points:

        M = ₍Y₂ - Y₁)/(X₂ - X₁).

• We were given point A (-2, 5) and provided the slope M = -1/2.

• Now a little Algebra: -1/2 = (5 - Y₁)/ (-2 - X₁)
• For simplicity sake we can break this down to (5 - Y₁) = -1 and (-2 - X₁) = 2
• We get X₁ = -4 and Y₁ = 6
• You can plot this or plug it back into our equation for the line to verify linear compliance.
• Thus Point B (-4, 6)

Answer 3

Hi Vazhin,

 

slope (change in y / change in x) = -1/2 

 

Point A = (-2,5)

 

Point B = Point A (x+2,y-1)

Point B = (-2+2,5-1)

Point B = (0,4)

 

Regards, Jordan.