Find the value of x for which the distance between the point P(x,4)and Q(9,10)is 10 units ?

Question

Answer

Answer

Finding the value of x for which the distance between the point P(x,4) and Q(9,10) is 10 units

Step 1: Use the distance formula to find the distance between points P and Q.

Step 2: Set the distance equal to 10 and solve for x.

Let's start by using the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Where:

x1 = x

y1 = 4

x2 = 9

y2 = 10

Substituting these values into the formula, we get:

d = sqrt((9 - x)^2 + (10 - 4)^2)

Next, we can simplify the equation by squaring both sides:

d^2 = (9 - x)^2 + (10 - 4)^2

Expanding the equation, we get:

d^2 = 81 - 18x + x^2 + 36

Combining like terms, we get:

d^2 = x^2 - 18x + 117

Now, we can set the distance equal to 10:

10^2 = x^2 - 18x + 117

Simplifying the equation, we get:

0 = x^2 - 18x + 17

Using the quadratic formula, we can solve for x:

x = (18 ± sqrt(18^2 - 4(1)(17))) / 2(1)

x = (18 ± sqrt(284)) / 2

x ≈ 0.561 or x ≈ 17.439

Therefore, the value of x for which the distance between the point P(x,4)and Q(9,10)is 10 units is approximately 0.561 or 17.439.

Answer

10 =81-18x+×*2+36
0=×*2-18×+117-100
×*2-18×+17=0
×*2- 17x-1×+17=0
×(×-17)-1(×-17)=0
(×-17)(×-1)=0
(×=17,1)

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