Final answer:
The value of a is 4, as the distance formula simplifies to the absolute value of the difference along the x-axis, which gives two solutions. Since E is in quadrant IV, which has positive x coordinates, a must be positive, leading to the solution a = 4.
Step-by-step explanation:
The question asks for the value of a given that the distance between points D(-3, -2) and E(a, -2) is 7, and point E is in quadrant IV of the Cartesian plane.
To find the value of a, we use the distance formula for two points on a coordinate plane, which is:
√[(x2 - x1)² + (y2 - y1)²]. In this case, since the y-coordinates are the same, the formula simplifies to just a - (-3) or a + 3 because the distance is only along the x-axis. Setting this equal to 7 and solving for a gives us two possible solutions, a = 4 or a = -10. Since point E is in quadrant IV, where x is positive and y is negative, we choose a = 4.