Question

what are the coordinates of vertex j on the image? a. (-1, -6) b. (1, -4) c. (-7, 3) d. (2, -7)

Explanation:

Step1: Recall coordinate system rules

In a coordinate system, the x - coordinate is the horizontal (left - right) position, and the y - coordinate is the vertical (up - down) position. For a point \((x,y)\), if \(x\) is negative, the point is to the left of the origin; if \(x\) is positive, it is to the right. If \(y\) is negative, the point is below the origin; if \(y\) is positive, it is above.

Step2: Analyze the options

• Option A: \((- 1,-6)\) - Let's assume the grid has a scale where each square is 1 unit. Looking at the position of vertex \(J'\), we check the horizontal and vertical distances.
• Option B: \((1, - 4)\) - The x - coordinate here is positive, but from the grid, the vertex \(J'\) should be to the left of the origin (negative x - coordinate), so B is incorrect.
• Option C: \((-7,3)\) - The y - coordinate here is positive, but the vertex \(J'\) is below the x - axis (negative y - coordinate), so C is incorrect.
• Option D: \((2,-7)\) - The x - coordinate is positive, and the vertex \(J'\) is to the left of the origin, so D is incorrect.

By looking at the grid (even with the partial view), the vertex \(J'\) has a negative x - coordinate and a negative y - coordinate. Among the options, \((-1,-6)\) (Option A) fits the pattern of a point with negative x and negative y, and the values are reasonable for the grid scale.

Answer:

A. \((-1, - 6)\)