The coordinates a(2, 1), b(7, 1), c(2, 4) form what type of polygon? a. an acute triangle b. an obtuse triangle c. a right triangle d. an isosceles triangle

 The correct option is (C) a right triangle.

Step-by-step explanation:  The given co-ordinates of a polygon are A(2, 1), B(7, 1), C(2, 4).

We are to select the correct type of the polygon.

Since we have the co-ordinates of the three points A, B and C, so the polygon will surely be a triangle.

Now, the lengths of the three sides AB, BC and CA of ΔABC can be calculated using distance formula as follows :

We have

This implies that

which is the Pythagorean triple. Hence, triangle ABC is a right-angled triangle.

Thus, (C) is the correct option.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

c

step-by-step explanation: