Question

Find a given that: a P(2, 3) and Q(a, -1) are 4 units apart b P(-1, 1) and Q(a, -2) are 5 units apart c X(a, a) is √√8 units from the origin d A(0, a) is equidistant from P(3, -3) and Q(-2, 2).​

Answer 1

To solve this problem, we can use the Pythagorean Theorem to solve for a.

For part (a), we know that P(2, 3) and Q(a, -1) are 4 units apart, so we can use the Pythagorean Theorem to calculate a:

(a - 2)² + (-1 - 3)² = 4²

Solving for a, we get:

a = 7

For part (b), we know that P(-1, 1) and Q(a, -2) are 5 units apart, so we can use the Pythagorean Theorem to calculate a:

(a + 1)² + (-2 - 1)² = 5²

Solving for a, we get:

a = 4

For part (c), we know that X(a, a) is √√8 units from the origin, so we can use the Pythagorean Theorem to calculate a:

a² + a² = 8

Solving for a, we get:

a = 2√2

For part (d), we know that A(0, a) is equidistant from P(3, -3) and Q(-2, 2), so we can use the Pythagorean Theorem to calculate a:

(3 - 0)² + (-3 - a)² = (-2 - 0)² + (2 - a)²

Solving for a, we get:

a = -1

Therefore, the value of a that satisfies all conditions is a = -1.

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