In triangle pqr, point x could represent

a) the incenter

b) the centroid

c) the orthocenter

d) the circumcenter

There's no picture attached. However we can define each point.

The incenter is the point where all three bisectors intercept, see the first image attached. Remember that a bisector is a line that divides angles in two equal parts.

The centroid of a triangle is the point where all three medians intercept, see the second image attached. A median is a line that goes from a vertex and divide its opposite in two equal parts.

The orthocenter is a point obtained by the interception of all three altitudes of a triangle, see the third image. An altitude is a line that goes from a vertex to the opposite side, forming a right triangle.

The circumcenter is the point formed by the interception of all three perpendicular bisectors of the triangle.

So, you just have to look and see if all three lines intercepting are medians, perpendicular bisectors, bisector or altitudes.

step-by-step explanation:

for exempl this   system of equations   y = x - 3

                                                                y = 2x - 5

look   the line : y = x -3     ( red)

                            the line : y = 2x -5 ( bleus)