Find the value of x so the line that passes through (x,2) and (-4, 5) is perpendicular to the line that passes through (4,8) and (2,-1)

x = 19/2

Step-by-step explanation:

The slopes of perpendicular lines have a product of -1.

Slope of line that passes through (4, 8) and (2, -1):

m1 = slope = (-1 - 8)/(2 - 4) = -9/(-2) = 9/2

Slope of perpendicular line is m2:

(m1)(m2) = -1

m2 = -1/m1 = -1/(9/2) = -2/9

The slope of the perpendicular line is -2/9

Now we write the expression for the slope of the second line. We use x for the unknown x-coordinate and -2/9 for the slope.

m2 = (5 - 2)/(-4 - x) = -2/9

3/(-4 - x) = -2/9

Cross multiply:

-2(-4 - x) = 3 * 9

8 + 2x = 27

2x = 19

x = 19/2

77

step-by-step explanation:

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.